//Demonstrates: Tangents are perpendicular to radii
public Page296Theorem7_1(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, -5); points.Add(r);
Point s = new Point("S", 8, -5); points.Add(s);
Point t = new Point("T", 0, -5); points.Add(t);
Segment ot = new Segment(o, t); segments.Add(ot);
List <Point> pnts = new List <Point>();
pnts.Add(r);
pnts.Add(t);
pnts.Add(s);
collinear.Add(new Collinear(pnts));
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment rs = (Segment)parser.Get(new Segment(r, s));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(t, c, rs));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
Intersection inter = parser.GetIntersection(ot, rs);
goals.Add(new Strengthened(inter, new Perpendicular(inter)));
}
//
// A \
// \ B
// \ /
// O \/ X
// /\
// / \
// C / D
//
// Two tangents:
// Intersection(X, AD, BC), Tangent(Circle(O), BC), Tangent(Circle(O), AD) -> 2 * Angle(AXC) = MajorArc(AC) - MinorArc(AC)
//
public static List <EdgeAggregator> InstantiateTwoTangentsTheorem(Tangent tangent1, Tangent tangent2, Intersection inter, GroundedClause original1, GroundedClause original2)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
CircleSegmentIntersection tan1 = tangent1.intersection as CircleSegmentIntersection;
CircleSegmentIntersection tan2 = tangent2.intersection as CircleSegmentIntersection;
if (tan1.StructurallyEquals(tan2))
{
return(newGrounded);
}
// Do the tangents apply to the same circle?
if (!tan1.theCircle.StructurallyEquals(tan2.theCircle))
{
return(newGrounded);
}
Circle circle = tan1.theCircle;
// Do these tangents work with this intersection?
if (!inter.HasSegment(tan1.segment) || !inter.HasSegment(tan2.segment))
{
return(newGrounded);
}
// Overkill? Do the tangents intersect at the same point as the intersection's intersect point?
if (!tan1.segment.FindIntersection(tan2.segment).StructurallyEquals(inter.intersect))
{
return(newGrounded);
}
//
// Get the arcs
//
Arc minorArc = new MinorArc(circle, tan1.intersect, tan2.intersect);
Arc majorArc = new MajorArc(circle, tan1.intersect, tan2.intersect);
Angle theAngle = new Angle(tan1.intersect, inter.intersect, tan2.intersect);
//
// Construct the new relationship
//
NumericValue two = new NumericValue(2);
GeometricAngleArcEquation gaaeq = new GeometricAngleArcEquation(new Multiplication(two, theAngle), new Subtraction(majorArc, minorArc));
// For hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(original1);
antecedent.Add(original2);
antecedent.Add(inter);
antecedent.Add(majorArc);
antecedent.Add(minorArc);
newGrounded.Add(new EdgeAggregator(antecedent, gaaeq, annotation));
return(newGrounded);
}
public TvPage1Prob6(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 8); points.Add(b);
Point c = new Point("C", 10, 8); points.Add(c);
Point d = new Point("D", 10, 0); points.Add(d);
Point o = new Point("O", 0, 2); points.Add(o);
Point p = new Point("P", 10, 4); points.Add(p);
Point q = new Point("Q", 0, 4); points.Add(q);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment da = new Segment(d, a); segments.Add(da);
List <Point> pnts = new List <Point>();
pnts.Add(b);
pnts.Add(q);
pnts.Add(o);
pnts.Add(a);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(c);
pnts.Add(p);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
Circle small = new Circle(o, 2);
Circle big = new Circle(p, 4);
circles.Add(small);
circles.Add(big);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(c, big, bc));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(d, big, da));
CircleSegmentIntersection cInter3 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, small, da));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
given.Add(new Strengthened(cInter3, new Tangent(cInter3)));
known.AddSegmentLength((Segment)parser.Get(new Segment(b, q)), 4);
known.AddSegmentLength((Segment)parser.Get(new Segment(c, d)), 8);
known.AddSegmentLength(bc, 10);
List <Point> unwanted = new List <Point>();
unwanted.Add(new Point("", -0.5, 2));
unwanted.Add(new Point("", 0.5, 2));
goalRegions = parser.implied.GetAllAtomicRegionsWithoutPoints(unwanted);
SetSolutionArea(80 + 6 * System.Math.PI);
problemName = "Tutor Vista Page 1 Problem 6";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page64(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 6, 4); points.Add(b);
Point c = new Point("C", 14, 4); points.Add(c);
Point d = new Point("D", 20, 0); points.Add(d);
Point o = new Point("O", 10, 4); points.Add(o);
Point p = new Point("P", 10, 0); points.Add(p);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment op = new Segment(o, p); segments.Add(op);
List <Point> pnts = new List <Point>();
pnts.Add(b);
pnts.Add(o);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(a);
pnts.Add(p);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 4);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Angle a1 = (Angle)parser.Get(new Angle(b, o, p));
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(p, circle, ad));
given.Add(new Strengthened(a1, new RightAngle(a1)));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
known.AddSegmentLength(ad, 20);
known.AddSegmentLength((Segment)parser.Get(new Segment(b, c)), 8);
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 5, 1));
wanted.Add(new Point("", 15, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(56 - 8 * System.Math.PI);
problemName = "Collected Learning Page 64";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
// ) | B
// ) |
// O )| S
// ) |
// ) |
// ) | A
// Tangent(Circle(O, R), Segment(A, B)), Intersection(OS, AB) -> Perpendicular(Segment(A,B), Segment(O, S))
//
public static List <EdgeAggregator> Instantiate(GroundedClause clause)
{
annotation.active = EngineUIBridge.JustificationSwitch.PERPENDICULAR_TO_RADIUS_IS_TANGENT;
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is CircleSegmentIntersection)
{
CircleSegmentIntersection newInter = clause as CircleSegmentIntersection;
foreach (Perpendicular oldPerp in candidatePerpendicular)
{
newGrounded.AddRange(InstantiateTheorem(newInter, oldPerp, oldPerp));
}
foreach (Strengthened oldStreng in candidateStrengthened)
{
newGrounded.AddRange(InstantiateTheorem(newInter, oldStreng.strengthened as Perpendicular, oldStreng));
}
candidateIntersections.Add(newInter);
}
else if (clause is Perpendicular)
{
Perpendicular newPerp = clause as Perpendicular;
foreach (CircleSegmentIntersection oldInter in candidateIntersections)
{
newGrounded.AddRange(InstantiateTheorem(oldInter, newPerp, newPerp));
}
candidatePerpendicular.Add(newPerp);
}
else if (clause is Strengthened)
{
Strengthened newStreng = clause as Strengthened;
if (!(newStreng.strengthened is Perpendicular))
{
return(newGrounded);
}
foreach (CircleSegmentIntersection oldInter in candidateIntersections)
{
newGrounded.AddRange(InstantiateTheorem(oldInter, newStreng.strengthened as Perpendicular, newStreng));
}
candidateStrengthened.Add(newStreng);
}
return(newGrounded);
}
// ) | B
// ) |
// O )| S
// ) |
// ) |
// ) | A
// Tangent(Circle(O, R), Segment(A, B)), Intersection(OS, AB) -> Perpendicular(Segment(A,B), Segment(O, S))
//
private static List <EdgeAggregator> InstantiateTheorem(CircleSegmentIntersection inter, Perpendicular perp, GroundedClause original)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
// The intersection points must be the same.
if (!inter.intersect.StructurallyEquals(perp.intersect))
{
return(newGrounded);
}
// Get the radius - if it exists
Segment radius = null;
Segment garbage = null;
inter.GetRadii(out radius, out garbage);
if (radius == null)
{
return(newGrounded);
}
// Two intersections, not a tangent situation.
if (garbage != null)
{
return(newGrounded);
}
// The radius can't be the same as the Circ-Inter segment.
if (inter.segment.HasSubSegment(radius))
{
return(newGrounded);
}
// Does this perpendicular apply to this Arc intersection?
if (!perp.HasSegment(radius) || !perp.HasSegment(inter.segment))
{
return(newGrounded);
}
Strengthened newTangent = new Strengthened(inter, new Tangent(inter));
// For hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(original);
antecedent.Add(inter);
newGrounded.Add(new EdgeAggregator(antecedent, newTangent, annotation));
return(newGrounded);
}
public Page10Prob36(bool onoff, bool complete) : base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 9); points.Add(b);
Point c = new Point("C", 8, 9); points.Add(c);
Point d = new Point("D", 12, 9); points.Add(d);
Point e = new Point("E", 12, 0); points.Add(e);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment de = new Segment(d, e); segments.Add(de);
Segment ea = new Segment(e, a); segments.Add(ea);
Point x = new Point("X", 4, 9.0); points.Add(x);
circles.Add(new Circle(x, 4.0));
List <Point> pts = new List <Point>();
pts.Add(b);
pts.Add(x);
pts.Add(c);
pts.Add(d);
collinear.Add(new Collinear(pts));
parser = new TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection csi = new CircleSegmentIntersection(b, circles[0], ab);
given.Add(new Tangent((CircleSegmentIntersection)parser.Get(csi)));
given.Add(new RightAngle((Angle)parser.Get(new Angle(b, a, e))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, d)), ea));
known.AddSegmentLength(ab, 9);
known.AddSegmentLength(cd, 4);
known.AddSegmentLength(ea, 12);
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 10, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(108 - 16 * System.Math.PI / 2.0);
problemName = "Glencoe Page 10 Problem 36";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
// ) | B
// ) |
// O )| S
// ) |
// ) |
// ) | A
// Tangent(Circle(O, R), Segment(A, B)), Intersection(OS, AB) -> Perpendicular(Segment(A,B), Segment(O, S))
//
private static List <EdgeAggregator> InstantiateTheorem(Tangent tangent, Intersection inter, GroundedClause original)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
CircleSegmentIntersection tanInter = tangent.intersection as CircleSegmentIntersection;
// Does this tangent segment apply to this intersection?
if (!inter.HasSegment(tanInter.segment))
{
return(newGrounded);
}
// Get the radius--if it exists
Segment radius = null;
Segment garbage = null;
tanInter.GetRadii(out radius, out garbage);
if (radius == null)
{
return(newGrounded);
}
// Does this radius apply to this intersection?
if (!inter.HasSubSegment(radius))
{
return(newGrounded);
}
Strengthened newPerp = new Strengthened(inter, new Perpendicular(inter));
// For hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(original);
antecedent.Add(inter);
newGrounded.Add(new EdgeAggregator(antecedent, newPerp, annotation));
return(newGrounded);
}
//Demonstrates: Tangents are perpendicular to radii
public Page296Theorem7_1_Test2(bool onoff, bool complete) : base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", 3, 4); points.Add(a);
Point p = new Point("P", 0, 6.25); points.Add(p);
Segment ap = new Segment(a, p); segments.Add(ap);
Segment ao = new Segment(a, o); segments.Add(ao);
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circle, ap));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
Intersection inter = parser.GetIntersection(ao, ap);
goals.Add(new Strengthened(inter, new Perpendicular(inter)));
}
//Demonstrates: ChordTangentAngleHalfInterceptedArc
public Test02(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, -5); points.Add(r);
Point s = new Point("S", 8, -5); points.Add(s);
Point t = new Point("T", 0, -5); points.Add(t);
Point u = new Point("U", -3, 4); points.Add(u);
Point v = new Point("V", 3, 4); points.Add(v);
Segment tu = new Segment(t, u); segments.Add(tu);
Segment tv = new Segment(t, v); segments.Add(tv);
List <Point> pnts = new List <Point>();
pnts.Add(r);
pnts.Add(t);
pnts.Add(s);
collinear.Add(new Collinear(pnts));
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
MinorArc m1 = (MinorArc)parser.Get(new MinorArc(c, t, u));
MinorArc m2 = (MinorArc)parser.Get(new MinorArc(c, t, v));
Segment rs = (Segment)parser.Get(new Segment(r, s));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(t, c, rs));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(r, t, u)), (Angle)parser.Get(new Angle(s, t, v))));
goals.Add(new GeometricCongruentArcs(m1, m2));
}
public HbPage2Prob4(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 10); points.Add(b);
Point c = new Point("C", 10, 10); points.Add(c);
Point d = new Point("D", 10, 0); points.Add(d);
Point o = new Point("O", 5, 5); points.Add(o);
Point e = new Point("E", 0, 5); points.Add(e);
Point f = new Point("F", 10, 5); points.Add(f);
//Segment ab = new Segment(a, b); segments.Add(ab);
Segment bc = new Segment(b, c); segments.Add(bc);
//Segment cd = new Segment(c, d); segments.Add(cd);
Segment da = new Segment(d, a); segments.Add(da);
List <Point> pnts = new List <Point>();
pnts.Add(b);
pnts.Add(o);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(a);
pnts.Add(o);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(a);
pnts.Add(e);
pnts.Add(b);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(c);
pnts.Add(f);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 5);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ab = (Segment)parser.Get(new Segment(a, b));
Segment cd = (Segment)parser.Get(new Segment(c, d));
Angle a1 = (Angle)parser.Get(new Angle(b, c, d));
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(e, circle, ab));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(f, circle, cd));
given.Add(new GeometricCongruentSegments(ab, bc));
given.Add(new GeometricCongruentSegments(ab, cd));
given.Add(new GeometricCongruentSegments(ab, da));
given.Add(new Strengthened(a1, new RightAngle(a1)));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
known.AddSegmentLength(ab, 10);
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 2, 9));
wanted.Add(new Point("", 8, 9));
wanted.Add(new Point("", 2, 1));
wanted.Add(new Point("", 8, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(50 - 12.5 * System.Math.PI);
problemName = "Hatboro Page 2 Problem 4";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page5Row5Prob17(bool onoff, bool complete) : base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 6); points.Add(b);
Point c = new Point("C", 6, 6); points.Add(c);
Point d = new Point("D", 6, 0); points.Add(d);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment da = new Segment(d, a); segments.Add(da);
Point x = new Point("X", 0, 3.0); points.Add(x);
Point y = new Point("Y", 6, 3.0); points.Add(y);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(x);
pts.Add(b);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(c);
pts.Add(y);
pts.Add(d);
collinear.Add(new Collinear(pts));
Circle circleX = new Circle(x, 3.0);
Circle circleY = new Circle(y, 3.0);
circles.Add(circleX);
circles.Add(circleY);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(b, circleX, bc));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(c, circleY, bc));
CircleSegmentIntersection cInter3 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circleX, da));
CircleSegmentIntersection cInter4 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(d, circleY, da));
given.Add(new GeometricCongruentSegments(da, (Segment)parser.Get(new Segment(a, b))));
given.Add(new GeometricCongruentSegments(da, (Segment)parser.Get(new Segment(c, d))));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
given.Add(new Strengthened(cInter3, new Tangent(cInter3)));
given.Add(new Strengthened(cInter4, new Tangent(cInter4)));
known.AddSegmentLength(da, 6);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, b)), 6);
known.AddSegmentLength((Segment)parser.Get(new Segment(c, d)), 6);
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 3, .5));
wanted.Add(new Point("", 3, 5.5));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(36 - System.Math.PI * 3 * 3);
problemName = "Jurgensen Page 5 Problem 17";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page5Row5Prob18(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 4); points.Add(b);
Point c = new Point("C", 0, 8); points.Add(c);
Point d = new Point("D", 20, 8); points.Add(d);
Point e = new Point("E", 18, 4); points.Add(e);
Point f = new Point("F", 16, 0); points.Add(f);
Point g = new Point("G", 16, 8); points.Add(g);
Point x = new Point("X", 8, 4); points.Add(x);
Point y = new Point("Y", 8, 0); points.Add(y);
Segment xy = new Segment(x, y); segments.Add(xy);
Segment fg = new Segment(f, g); segments.Add(fg);
Circle circle = new Circle(x, 4.0);
circles.Add(circle);
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(b);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(c);
pts.Add(g);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(d);
pts.Add(e);
pts.Add(f);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(b);
pts.Add(x);
pts.Add(e);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(a);
pts.Add(y);
pts.Add(f);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Angle angle = (Angle)parser.Get(new Angle(a, c, d));
Triangle tri = (Triangle)parser.Get(new Triangle(f, g, d));
CircleSegmentIntersection inter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(y, circle, (Segment)parser.Get(new Segment(a, f))));
given.Add(new Strengthened(angle, new RightAngle(angle)));
given.Add(new Strengthened(inter, new Tangent(inter)));
given.Add(new Strengthened(tri, new RightTriangle(tri)));
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(c, d)), (Segment)parser.Get(new Segment(b, e))));
given.Add(new GeometricParallel((Segment)parser.Get(new Segment(c, d)), (Segment)parser.Get(new Segment(a, f))));
given.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(d, e)), (Segment)parser.Get(new Segment(e, f))));
known.AddSegmentLength((Segment)parser.Get(new Segment(a, f)), 16);
known.AddSegmentLength((Segment)parser.Get(new Segment(c, d)), 20);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, c)), 8);
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 1, 1));
wanted.Add(new Point("", 15, 1));
wanted.Add(new Point("", 3, 7));
wanted.Add(new Point("", 10, 5));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(144 - System.Math.PI * 8);
}
//
// Find every point of intersection among segments (if they are not labeled in the UI) -- name them.
//
public List <CircleSegmentIntersection> FindCircleSegmentIntersections()
{
List <CircleSegmentIntersection> intersections = new List <CircleSegmentIntersection>();
foreach (GeometryTutorLib.ConcreteAST.Circle circle in implied.circles)
{
foreach (GeometryTutorLib.ConcreteAST.Segment segment in implied.segments)
{
Point inter1 = null;
Point inter2 = null;
circle.FindIntersection(segment, out inter1, out inter2);
if (!segment.PointLiesOnAndBetweenEndpoints(inter1))
{
inter1 = null;
}
if (!segment.PointLiesOnAndBetweenEndpoints(inter2))
{
inter2 = null;
}
// Analyze this segment w.r.t. to this circle: tangent, secant, chord.
if (inter1 != null || inter2 != null)
{
circle.AnalyzeSegment(segment, implied.allFigurePoints);
}
}
}
foreach (GeometryTutorLib.ConcreteAST.Circle circle in implied.circles)
{
foreach (GeometryTutorLib.ConcreteAST.Segment segment in implied.maximalSegments)
{
//
// Find any intersection points between the circle and the segment;
// the intersection MUST be between the segment endpoints
//
Point inter1 = null;
Point inter2 = null;
circle.FindIntersection(segment, out inter1, out inter2);
if (!segment.PointLiesOnAndBetweenEndpoints(inter1))
{
inter1 = null;
}
if (!segment.PointLiesOnAndBetweenEndpoints(inter2))
{
inter2 = null;
}
// Add them to the list (possibly)
List <Point> intersectionPts = new List <Point>();
if (inter1 != null)
{
intersectionPts.Add(inter1);
}
if (inter2 != null)
{
intersectionPts.Add(inter2);
}
// normalized to drawing point (names)
intersectionPts = implied.NormalizePointsToDrawing(intersectionPts);
// and add to each figure (circle and polygon).
circle.AddIntersectingPoints(intersectionPts);
//
// Construct the intersections
//
CircleSegmentIntersection csInter = null;
if (intersectionPts.Any())
{
csInter = new CircleSegmentIntersection(intersectionPts[0], circle, segment);
GeometryTutorLib.Utilities.AddStructurallyUnique <CircleSegmentIntersection>(intersections, csInter);
}
if (intersectionPts.Count > 1)
{
csInter = new CircleSegmentIntersection(intersectionPts[1], circle, segment);
GeometryTutorLib.Utilities.AddStructurallyUnique <CircleSegmentIntersection>(intersections, csInter);
}
}
// Complete any processing attributed to the circle and all the segments.
circle.CleanUp();
}
return(intersections);
}
public Page7Prob26(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 4); points.Add(b);
Point c = new Point("C", 4, 4); points.Add(c);
Point d = new Point("D", 4, 0); points.Add(d);
Point o = new Point("O", 2, 2); points.Add(o);
Point p = new Point("P", 0, 2); points.Add(p);
Point q = new Point("Q", 4, 2); points.Add(q);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment da = new Segment(d, a); segments.Add(da);
List <Point> pts = new List <Point>();
pts.Add(a); pts.Add(p); pts.Add(b);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(p); pts.Add(o); pts.Add(q);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(c); pts.Add(q); pts.Add(d);
collinear.Add(new Collinear(pts));
Circle circle = new Circle(o, 2);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment cd = (Segment)parser.Get(new Segment(c, d));
Angle a1 = (Angle)parser.Get(new Angle(a, b, c));
Angle a2 = (Angle)parser.Get(new Angle(b, c, d));
Angle a3 = (Angle)parser.Get(new Angle(c, d, a));
Angle a4 = (Angle)parser.Get(new Angle(d, a, b));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(q, circle, cd));
known.AddSegmentLength(da, 4);
known.AddSegmentLength(cd, 4);
given.Add(new Strengthened(a1, new RightAngle(a1)));
given.Add(new Strengthened(a2, new RightAngle(a2)));
given.Add(new Strengthened(a3, new RightAngle(a3)));
given.Add(new Strengthened(a4, new RightAngle(a4)));
given.Add(new GeometricSegmentEquation(da, new NumericValue(4)));
given.Add(new GeometricSegmentEquation(cd, new NumericValue(4)));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
List <Point> unwanted = new List <Point>();
unwanted.Add(new Point("", 0.1, 3.8));
unwanted.Add(new Point("", 3.9, 3.8));
goalRegions = parser.implied.GetAllAtomicRegionsWithoutPoints(unwanted);
SetSolutionArea(8 + 2 * System.Math.PI);
problemName = "McDougall Page 7 Problem 24";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
// A
// |)
// | )
// | )
// Q------- O---X---) D
// | )
// | )
// |)
// C
//
// Perpendicular(Segment(Q, D), Segment(A, C)) -> Congruent(Arc(A, D), Arc(D, C)) -> Congruent(Segment(AX), Segment(XC))
//
private static List <EdgeAggregator> InstantiateTheorem(Intersection inter, CircleSegmentIntersection arcInter, Perpendicular perp, GroundedClause original)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
//
// Does this intersection apply to this perpendicular?
//
if (!inter.intersect.StructurallyEquals(perp.intersect))
{
return(newGrounded);
}
// Is this too restrictive?
if (!((inter.HasSegment(perp.lhs) && inter.HasSegment(perp.rhs)) && (perp.HasSegment(inter.lhs) && perp.HasSegment(inter.rhs))))
{
return(newGrounded);
}
//
// Does this perpendicular intersection apply to a given circle?
//
// Acquire the circles for which the segments are secants.
List <Circle> secantCircles1 = Circle.GetSecantCircles(perp.lhs);
List <Circle> secantCircles2 = Circle.GetSecantCircles(perp.rhs);
List <Circle> intersection = Utilities.Intersection <Circle>(secantCircles1, secantCircles2);
if (!intersection.Any())
{
return(newGrounded);
}
//
// Find the single, unique circle that has as chords the components of the perpendicular intersection
//
Circle theCircle = null;
Segment chord1 = null;
Segment chord2 = null;
foreach (Circle circle in intersection)
{
chord1 = circle.GetChord(perp.lhs);
chord2 = circle.GetChord(perp.rhs);
if (chord1 != null && chord2 != null)
{
theCircle = circle;
break;
}
}
Segment diameter = chord1.Length > chord2.Length ? chord1 : chord2;
Segment chord = chord1.Length < chord2.Length ? chord1 : chord2;
//
// Does the arc intersection apply?
//
if (!arcInter.HasSegment(diameter))
{
return(newGrounded);
}
if (!theCircle.StructurallyEquals(arcInter.theCircle))
{
return(newGrounded);
}
//
// Create the bisector
//
Strengthened sb = new Strengthened(inter, new SegmentBisector(inter, diameter));
Strengthened ab = new Strengthened(arcInter, new ArcSegmentBisector(arcInter));
// For hypergraph
List <GroundedClause> antecedentArc = new List <GroundedClause>();
antecedentArc.Add(arcInter);
antecedentArc.Add(original);
antecedentArc.Add(theCircle);
newGrounded.Add(new EdgeAggregator(antecedentArc, ab, annotation));
List <GroundedClause> antecedentSegment = new List <GroundedClause>();
antecedentSegment.Add(inter);
antecedentSegment.Add(original);
antecedentSegment.Add(theCircle);
newGrounded.Add(new EdgeAggregator(antecedentSegment, sb, annotation));
return(newGrounded);
}
public Page8Prob39(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", -3.5, -3.5); points.Add(a);
Point b = new Point("B", -3.5, 3.5); points.Add(b);
Point c = new Point("C", 3.5, 3.5); points.Add(c);
Point d = new Point("D", 3.5, -3.5); points.Add(d);
Point e = new Point("E", -1.5, 1.5 / System.Math.Sqrt(3)); points.Add(e);
Point f = new Point("F", 1.5, 1.5 / System.Math.Sqrt(3)); points.Add(f);
Point g = new Point("G", 0, 3 / System.Math.Sqrt(3)); points.Add(g);
Point w = new Point("W", 0, -3.5); points.Add(w);
Point x = new Point("X", -3.5, 0); points.Add(x);
Point y = new Point("Y", 0, 3.5); points.Add(y);
Point z = new Point("W", 3.5, 0); points.Add(w);
//Segment ab = new Segment(a, b); segments.Add(ab);
//Segment bc = new Segment(b, c); segments.Add(bc);
//Segment cd = new Segment(c, d); segments.Add(cd);
//Segment da = new Segment(d, a); segments.Add(da);
Segment ef = new Segment(e, f); segments.Add(ef);
Segment fg = new Segment(f, g); segments.Add(fg);
Segment ge = new Segment(g, e); segments.Add(ge);
List <Point> pnts = new List <Point>();
pnts.Add(a); pnts.Add(x); pnts.Add(b);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(b); pnts.Add(y); pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(c); pnts.Add(z); pnts.Add(d);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(d); pnts.Add(w); pnts.Add(a);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 3.5);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, b)), 7);
known.AddSegmentLength(ef, 3);
given.Add(new GeometricCongruentSegments(ef, fg));
given.Add(new GeometricCongruentSegments(ef, ge));
Angle angle = (Angle)parser.Get(new Angle(b, a, d));
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(x, circle,
(Segment)parser.Get(new Segment(a, b))));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(y, circle,
(Segment)parser.Get(new Segment(b, c))));
CircleSegmentIntersection cInter3 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(z, circle,
(Segment)parser.Get(new Segment(c, d))));
CircleSegmentIntersection cInter4 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(w, circle,
(Segment)parser.Get(new Segment(d, a))));
given.Add(new Strengthened(angle, new RightAngle(angle)));
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 3, 0));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea((12.25 * System.Math.PI) - (1.5 * System.Math.Sqrt(6.75)));
problemName = "Glencoe Page 8 Problem 39";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
//
// C
// /)
// / )
// / )
// / )
// A /)_________ B
//
// Tangent(Circle(O), Segment(AB)), Intersection(Segment(AC), Segment(AB)) -> 2 * Angle(CAB) = Arc(C, B)
//
public static List <EdgeAggregator> InstantiateTheorem(Intersection inter, Tangent tangent, GroundedClause original)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
CircleSegmentIntersection tan = tangent.intersection as CircleSegmentIntersection;
//
// Does this tangent apply to this intersection?
//
if (!inter.intersect.StructurallyEquals(tangent.intersection.intersect))
{
return(newGrounded);
}
Segment secant = null;
Segment tanSegment = null;
if (tan.HasSegment(inter.lhs))
{
secant = inter.rhs;
tanSegment = inter.lhs;
}
else if (tan.HasSegment(inter.rhs))
{
secant = inter.lhs;
tanSegment = inter.rhs;
}
else
{
return(newGrounded);
}
//
// Acquire the angle and intercepted arc.
//
Segment chord = tan.theCircle.GetChord(secant);
if (chord == null)
{
return(newGrounded);
}
//Segment chord = tan.theCircle.ContainsChord(secant);
// Arc
// We want the MINOR ARC only!
if (tan.theCircle.DefinesDiameter(chord))
{
Arc theArc = null;
Point midpt = PointFactory.GeneratePoint(tan.theCircle.Midpoint(chord.Point1, chord.Point2));
Point opp = PointFactory.GeneratePoint(tan.theCircle.OppositePoint(midpt));
Point tanPoint = tanSegment.OtherPoint(inter.intersect);
if (tanPoint != null)
{
// Angle; the smaller angle is always the chosen angle
Angle theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanPoint);
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, midpt, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, opp, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
}
else
{
// Angle; the smaller angle is always the chosen angle
Angle theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanSegment.Point1);
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, midpt, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, opp, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
// Angle; the smaller angle is always the chosen angle
theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanSegment.Point2);
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, midpt, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, opp, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
}
}
else
{
Arc theArc = new MinorArc(tan.theCircle, chord.Point1, chord.Point2);
// Angle; the smaller angle is always the chosen angle
Point endPnt = (inter.intersect.StructurallyEquals(tanSegment.Point1)) ? tanSegment.Point2 : tanSegment.Point1;
Angle theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, endPnt);
if (theAngle.measure > 90)
{
//If the angle endpoint was already set to Point2, or if the intersect equals Point2, then the smaller angle does not exist
//In this case, should we create a major arc or return nothing?
if (endPnt.StructurallyEquals(tanSegment.Point2) || inter.intersect.StructurallyEquals(tanSegment.Point2))
{
return(newGrounded);
}
theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanSegment.Point2);
}
Multiplication product = new Multiplication(new NumericValue(2), theAngle);
GeometricAngleArcEquation angArcEq = new GeometricAngleArcEquation(product, theArc);
// For hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(original);
antecedent.Add(inter);
antecedent.Add(theArc);
antecedent.Add(theAngle);
newGrounded.Add(new EdgeAggregator(antecedent, angArcEq, annotation));
}
return(newGrounded);
}
//Demonstrates: ExteriorAngleHalfDifferenceInterceptedArcs : two tangents
//Demonstrates: Tangents from point are congruent
public Test05(bool onoff, bool complete)
: base(onoff, complete)
{
//Circle
Point o = new Point("O", 0, 0); points.Add(o);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
//Intersection point for two tangents
Point c = new Point("C", 0, 6.25); points.Add(c);
//Points for tangent line ac, intersection at b
Point a = new Point("A", -8, 0.25); points.Add(a);
Point b = new Point("B", -3, 4); points.Add(b);
//Points for tangent line ec, intersection at d
Point e = new Point("E", 8, 0.25); points.Add(e);
Point d = new Point("D", 3, 4); points.Add(d);
//Create point for another arc (Arc(DF)) of equal measure to (1/2)*(MajorArc(BD)-MinorArc(BD))
MinorArc minor = new MinorArc(circleO, b, d);
MajorArc major = new MajorArc(circleO, b, d);
double measure = (major.GetMajorArcMeasureDegrees() - minor.GetMinorArcMeasureDegrees()) / 2;
//Get theta for D and E
Circle unit = new Circle(o, 1.0);
Point inter1, trash;
unit.FindIntersection(new Segment(o, d), out inter1, out trash);
if (inter1.X < 0)
{
inter1 = trash;
}
double dThetaDegrees = (System.Math.Acos(inter1.X)) * (180 / System.Math.PI);
double fThetaRadians = (dThetaDegrees - measure) * (System.Math.PI / 180);
//Get coordinates for E
Point unitPnt = new Point("", System.Math.Cos(fThetaRadians), System.Math.Sin(fThetaRadians));
Point f;
circleO.FindIntersection(new Segment(o, unitPnt), out f, out trash);
if (f.X < 0)
{
f = trash;
}
f = new Point("F", f.X, f.Y); points.Add(f);
//Should now be able to form segments for a central angle of equal measure to (1/2)*(Arc(AB)-Arc(CD))
Segment od = new Segment(o, d); segments.Add(od);
Segment of = new Segment(o, f); segments.Add(of);
List <Point> pnts = new List <Point>();
pnts.Add(a);
pnts.Add(b);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(c);
pnts.Add(d);
pnts.Add(e);
collinear.Add(new Collinear(pnts));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ac = (Segment)parser.Get(new Segment(a, c));
Segment ce = (Segment)parser.Get(new Segment(c, e));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(b, circleO, ac));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(d, circleO, ce));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
MinorArc a1 = (MinorArc)parser.Get(new MinorArc(circleO, b, d));
MajorArc a2 = (MajorArc)parser.Get(new MajorArc(circleO, b, d));
MinorArc centralAngleArc = (MinorArc)parser.Get(new MinorArc(circleO, d, f));
given.Add(new GeometricArcEquation(new Multiplication(new NumericValue(2), centralAngleArc), new Subtraction(a2, a1)));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, c, e)), (Angle)parser.Get(new Angle(d, o, f))));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, c)), (Segment)parser.Get(new Segment(c, d))));
}
public Page8Prob15(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 5); points.Add(b);
Point c = new Point("C", 10, 5); points.Add(c);
Point d = new Point("D", 10, 0); points.Add(d);
Point o = new Point("O", 2.5, 2.5); points.Add(o);
Point p = new Point("P", 2.5, 5); points.Add(p);
Point q = new Point("Q", 2.5, 0); points.Add(q);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
List <Point> pnts = new List <Point>();
pnts.Add(b);
pnts.Add(p);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(a);
pnts.Add(q);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(p);
pnts.Add(o);
pnts.Add(q);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 2.5);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Angle rA = (Angle)parser.Get(new Angle(a, d, c));
Segment bc = (Segment)parser.Get(new Segment(b, c));
Segment ad = (Segment)parser.Get(new Segment(a, d));
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(p, circle, bc));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(q, circle, ad));
known.AddSegmentLength((Segment)parser.Get(new Segment(c, d)), 5);
known.AddSegmentLength(ad, 10);
known.AddAngleMeasureDegree(rA, 90);
given.Add(new Strengthened(rA, new RightAngle(rA)));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
//Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ab, cd, bc, ad));
//given.Add(new Strengthened(quad, new Rectangle(quad)));
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 0.5, 4.5));
wanted.Add(new Point("", 0.1, 0.1));
wanted.Add(new Point("", 7, 3));
wanted.Add(new Point("", 7, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(50 - 6.25 * System.Math.PI);
problemName = "Glencoe Page 8 Problem 15";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page86Prob13(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", -5.5, 12); points.Add(b);
Point c = new Point("C", 14.5, 12); points.Add(c);
Point d = new Point("D", 9, 0); points.Add(d);
Point o = new Point("O", 4.5, 12); points.Add(o);
Point p = new Point("P", 4.5, 6); points.Add(p);
Point q = new Point("Q", 4.5, 0); points.Add(q);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
List <Point> pnts = new List <Point>();
pnts.Add(b);
pnts.Add(o);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(a);
pnts.Add(q);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(o);
pnts.Add(p);
pnts.Add(q);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(p, 6);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Segment bc = (Segment)parser.Get(new Segment(b, c));
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(q, circle, ad));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(o, circle, bc));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
known.AddSegmentLength(ad, 9);
//This top base was length 10 in the original problem, but this wouldn't actually be possible since the
//inscribed circle has a total diameter of length 12. So changed the top base to length 20.
known.AddSegmentLength(bc, 20);
known.AddSegmentLength((Segment)parser.Get(new Segment(o, p)), 6);
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 0.5, 0.2));
wanted.Add(new Point("", -0.3, 11));
wanted.Add(new Point("", 9.2, 11));
wanted.Add(new Point("", 8.5, 0.2));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(174 - 36 * System.Math.PI);
problemName = "Collected Learning Page 86 Prob 13";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
//Demonstrates: ExteriorAngleHalfDifferenceInterceptedArcs : one tangent, one secant
public Test06(bool onoff, bool complete)
: base(onoff, complete)
{
//Circle
Point o = new Point("O", 0, 0); points.Add(o);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
//Intersection point for tangent & secant
Point c = new Point("C", 0, 6.25); points.Add(c);
//Points for tangent line ac, intersection at b
Point a = new Point("A", -8, 0.25); points.Add(a);
Point b = new Point("B", -3, 4); points.Add(b);
//Points for secant line ce, intersections at D & E
Point d = new Point("D", 0, 5); points.Add(d);
Point e = new Point("E", 0, -5); points.Add(e);
//Create point for another arc (Arc(DF)) of equal measure to (1/2)*(MinorArc(BE)-MinorArc(BD))
MinorArc farMinor = new MinorArc(circleO, b, e);
MinorArc closeMinor = new MinorArc(circleO, b, d);
double measure = (farMinor.GetMinorArcMeasureDegrees() - closeMinor.GetMinorArcMeasureDegrees()) / 2;
//Get theta for F
double dThetaDegrees = 90;
double fThetaRadians = (dThetaDegrees - measure) * (System.Math.PI / 180);
//Get coordinates for F
Point unitPnt = new Point("", System.Math.Cos(fThetaRadians), System.Math.Sin(fThetaRadians));
Point f, trash;
circleO.FindIntersection(new Segment(o, unitPnt), out f, out trash);
if (f.X < 0)
{
f = trash;
}
f = new Point("F", f.X, f.Y); points.Add(f);
//Should now be able to form segments for a central angle of equal measure to (1/2)*(Arc(AB)-Arc(CD))
Segment od = new Segment(o, d); segments.Add(od);
Segment of = new Segment(o, f); segments.Add(of);
List <Point> pnts = new List <Point>();
pnts.Add(a);
pnts.Add(b);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List <Point>();
pnts.Add(c);
pnts.Add(d);
pnts.Add(e);
collinear.Add(new Collinear(pnts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ac = (Segment)parser.Get(new Segment(a, c));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(b, circleO, ac));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
MinorArc far = (MinorArc)parser.Get(new MinorArc(circleO, b, e));
MinorArc close = (MinorArc)parser.Get(new MinorArc(circleO, b, d));
MinorArc centralAngleArc = (MinorArc)parser.Get(new MinorArc(circleO, d, f));
given.Add(new GeometricArcEquation(new Multiplication(new NumericValue(2), centralAngleArc), new Subtraction(far, close)));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, c, e)), (Angle)parser.Get(new Angle(d, o, f))));
}
public Page8Row6Prob42(bool onoff, bool complete)
: base(onoff, complete)
{
//Square vertices
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 6); points.Add(b);
Point c = new Point("C", 6, 6); points.Add(c);
Point d = new Point("D", 6, 0); points.Add(d);
//Circle centers
Point q = new Point("Q", 1.5, 1.5); points.Add(q);
Point r = new Point("R", 1.5, 4.5); points.Add(r);
Point s = new Point("S", 4.5, 4.5); points.Add(s);
Point t = new Point("T", 4.5, 1.5); points.Add(t);
//Circle-Square intersections
Point e = new Point("E", 0, 1.5); points.Add(e);
Point f = new Point("F", 0, 4.5); points.Add(f);
Point g = new Point("G", 1.5, 6); points.Add(g);
Point h = new Point("H", 4.5, 6); points.Add(h);
Point i = new Point("I", 6, 4.5); points.Add(i);
Point j = new Point("J", 6, 1.5); points.Add(j);
Point k = new Point("K", 4.5, 0); points.Add(k);
Point l = new Point("L", 1.5, 0); points.Add(l);
//Circle-circle intersections
Point m = new Point("M", 1.5, 3); points.Add(m);
Point n = new Point("N", 3, 4.5); points.Add(n);
Point o = new Point("O", 4.5, 3); points.Add(o);
Point p = new Point("P", 3, 1.5); points.Add(p);
//Square sides
List <Point> pts = new List <Point>();
pts.Add(a);
pts.Add(e);
pts.Add(f);
pts.Add(b);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(b);
pts.Add(g);
pts.Add(h);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(c);
pts.Add(i);
pts.Add(j);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(d);
pts.Add(k);
pts.Add(l);
pts.Add(a);
collinear.Add(new Collinear(pts));
//Diameters
pts = new List <Point>();
pts.Add(f);
pts.Add(r);
pts.Add(n);
pts.Add(s);
pts.Add(i);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(e);
pts.Add(q);
pts.Add(p);
pts.Add(t);
pts.Add(j);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(g);
pts.Add(r);
pts.Add(m);
pts.Add(q);
pts.Add(l);
collinear.Add(new Collinear(pts));
pts = new List <Point>();
pts.Add(h);
pts.Add(s);
pts.Add(o);
pts.Add(t);
pts.Add(k);
collinear.Add(new Collinear(pts));
Circle tLeft = new Circle(r, 1.5);
Circle bLeft = new Circle(q, 1.5);
Circle tRight = new Circle(s, 1.5);
Circle bRight = new Circle(t, 1.5);
circles.Add(tLeft);
circles.Add(bLeft);
circles.Add(tRight);
circles.Add(bRight);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, b)), 6);
Segment ab = (Segment)parser.Get(new Segment(a, b));
Segment bc = (Segment)parser.Get(new Segment(b, c));
Segment cd = (Segment)parser.Get(new Segment(c, d));
Segment ad = (Segment)parser.Get(new Segment(a, d));
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(e, bLeft, ab));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(f, tLeft, ab));
CircleSegmentIntersection cInter3 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(g, tLeft, bc));
CircleSegmentIntersection cInter4 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(h, tRight, bc));
CircleSegmentIntersection cInter5 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(i, tRight, cd));
CircleSegmentIntersection cInter6 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(j, bRight, cd));
CircleSegmentIntersection cInter7 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(k, bRight, ad));
CircleSegmentIntersection cInter8 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(l, bLeft, ad));
CircleCircleIntersection cInter9 = (CircleCircleIntersection)parser.Get(new CircleCircleIntersection(m, tLeft, bLeft));
CircleCircleIntersection cInter10 = (CircleCircleIntersection)parser.Get(new CircleCircleIntersection(n, tLeft, tRight));
CircleCircleIntersection cInter11 = (CircleCircleIntersection)parser.Get(new CircleCircleIntersection(o, tRight, bRight));
CircleCircleIntersection cInter12 = (CircleCircleIntersection)parser.Get(new CircleCircleIntersection(p, bLeft, bRight));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
given.Add(new Strengthened(cInter3, new Tangent(cInter3)));
given.Add(new Strengthened(cInter4, new Tangent(cInter4)));
given.Add(new Strengthened(cInter5, new Tangent(cInter5)));
given.Add(new Strengthened(cInter6, new Tangent(cInter6)));
given.Add(new Strengthened(cInter7, new Tangent(cInter7)));
given.Add(new Strengthened(cInter8, new Tangent(cInter8)));
given.Add(new Strengthened(cInter9, new Tangent(cInter9)));
given.Add(new Strengthened(cInter10, new Tangent(cInter10)));
given.Add(new Strengthened(cInter11, new Tangent(cInter11)));
given.Add(new Strengthened(cInter12, new Tangent(cInter12)));
given.Add(new GeometricCongruentCircles(tLeft, bLeft));
given.Add(new GeometricCongruentCircles(tLeft, tRight));
given.Add(new GeometricCongruentCircles(tLeft, bRight));
List <Point> wanted = new List <Point>();
wanted.Add(new Point("", 0.1, 0.1));
wanted.Add(new Point("", 0.1, 3));
wanted.Add(new Point("", 0.1, 5.9));
wanted.Add(new Point("", 3, 5.9));
wanted.Add(new Point("", 3, 3));
wanted.Add(new Point("", 3, 0.1));
wanted.Add(new Point("", 5.9, 0.1));
wanted.Add(new Point("", 5.9, 3));
wanted.Add(new Point("", 5.9, 5.9));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(36 - (9 * System.Math.PI));
problemName = "Glencoe Page 8 Row 6 Problem 42";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
//
// A \
// \ B
// \ /
// O \/ X
// /\
// / \
// C / D
//
// One Secant, One Tangent
// Intersection(X, AD, BC), Tangent(Circle(O), BC) -> 2 * Angle(AXC) = MajorArc(AC) - MinorArc(AC)
//
public static List <EdgeAggregator> InstantiateOneSecantOneTangentTheorem(Intersection inter, Tangent tangent, GroundedClause original)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
CircleSegmentIntersection tan = tangent.intersection as CircleSegmentIntersection;
// Is the tangent segment part of the intersection?
if (!inter.HasSegment(tan.segment))
{
return(newGrounded);
}
// Acquire the chord that the intersection creates.
Segment secant = inter.OtherSegment(tan.segment);
Circle circle = tan.theCircle;
Segment chord = circle.ContainsChord(secant);
// Check if this segment never intersects the circle or doesn't create a chord.
if (chord == null)
{
return(newGrounded);
}
//
// Get the near / far points out of the chord
//
Point closeChordPt = null;
Point farChordPt = null;
if (Segment.Between(chord.Point1, chord.Point2, inter.intersect))
{
closeChordPt = chord.Point1;
farChordPt = chord.Point2;
}
else
{
closeChordPt = chord.Point2;
farChordPt = chord.Point1;
}
//
// Acquire the arcs
//
// Get the close arc first which we know exactly how it is constructed AND that it's a minor arc.
Arc closeArc = Arc.GetFigureMinorArc(circle, closeChordPt, tan.intersect);
// The far arc MAY be a major arc; if it is, the first candidate arc will contain the close arc.
Arc farArc = Arc.GetFigureMinorArc(circle, farChordPt, tan.intersect);
if (farArc.HasMinorSubArc(closeArc))
{
farArc = Arc.GetFigureMajorArc(circle, farChordPt, tan.intersect);
}
Angle theAngle = Angle.AcquireFigureAngle(new Angle(closeChordPt, inter.intersect, tan.intersect));
//
// Construct the new relationship
//
NumericValue two = new NumericValue(2);
GeometricAngleArcEquation gaaeq = new GeometricAngleArcEquation(new Multiplication(two, theAngle), new Subtraction(farArc, closeArc));
// For hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(original);
antecedent.Add(inter);
antecedent.Add(closeArc);
antecedent.Add(farArc);
newGrounded.Add(new EdgeAggregator(antecedent, gaaeq, annotation));
return(newGrounded);
}
