// \ A
// \
// \
// center: O / P
// /
// / B
//
// Tangent(Circle(O), Segment(B, P)),
// Tangent(Circle(O), Segment(A, P)),
// Intersection(AP, BP) -> Congruent(Segment(A, P), Segment(P, B))
//
private static List<EdgeAggregator> InstantiateTheorem(Tangent tangent1, Tangent tangent2, Intersection inter, GroundedClause original1, GroundedClause original2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Do the tangents apply to the same circle?
if (!tangent1.intersection.theCircle.StructurallyEquals(tangent2.intersection.theCircle)) return newGrounded;
// Do the tangents have components the are part of the third intersection
if (!inter.HasSegment((tangent1.intersection as CircleSegmentIntersection).segment)) return newGrounded;
if (!inter.HasSegment((tangent2.intersection as CircleSegmentIntersection).segment)) return newGrounded;
Segment segment1 = Segment.GetFigureSegment(inter.intersect, tangent1.intersection.intersect);
Segment segment2 = Segment.GetFigureSegment(inter.intersect, tangent2.intersection.intersect);
GeometricCongruentSegments gcs = new GeometricCongruentSegments(segment1, segment2);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original1);
antecedent.Add(original2);
antecedent.Add(inter);
newGrounded.Add(new EdgeAggregator(antecedent, gcs, annotation));
return newGrounded;
}
//
// 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;
}
// ) | 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;
}
//
// 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;
}
//
// 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;
}