// ) | 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;
}
// 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;
}