public override bool Equals(Object obj)
{
CircleSegmentIntersection inter = obj as CircleSegmentIntersection;
if (inter == null)
{
return(false);
}
return(this.segment.Equals(inter.segment) &&
this.intersect.StructurallyEquals(inter.intersect) &&
this.theCircle.StructurallyEquals(inter.theCircle));
}
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(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 ArcSegmentBisector(CircleSegmentIntersection b)
: base()
{
bisected = b;
}
// 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 ArcSegmentBisector(CircleSegmentIntersection b) : base()
{
bisected = b;
}
//
// 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;
}
