Wallace-Simson-Gerader
Author: R. Albers

Der Satz von Wallace bzw. Simson

Gegeben sei ein Dreieck ABC

A = (1.46, -3.1)
B = (9.4, -3.08)
i1 = LineBisector(A, B)
C = (7.66, 2.84)
g = Circle(A, B, C)
P = Point(g)
j1 = LineBisector(B, C)
M = Intersect(j1, i1)
l1 = Ray(M, P)
k1 = CircleArc(M, C, A)
poly1, a, b, c = Polygon(A, B, C)
d = Line(A, B)
e = Line(B, C)
f = Line(C, A)
P_b = Intersect(k1, l1)
h = OrthogonalLine(P, d)
i = OrthogonalLine(P, f)
j = OrthogonalLine(P, e)
F_c = Intersect(d, h)
F_b = Intersect(i, f)
F_a = Intersect(j, e)
k = Circle(F_c, F_b, P_b)
p = Circle(P_b, F_b, F_a)
l = Segment(A, P_b)
m = Segment(P_b, C)
n = Line(F_c, F_a)
k3 = CircleArc(M, B, C)
k2 = CircleArc(M, A, B)
P_a = Intersect(k3, l1)
q = OrthogonalLine(P_a, e)
r = OrthogonalLine(P_a, f)
s = OrthogonalLine(P_a, d)
F_{aa} = Intersect(q, e)
F_{ba} = Intersect(r, f)
F_{ca} = Intersect(s, d)
poly2, t, a1, b1 = Polygon(F_{ba}, F_{aa}, C)
poly3, c1, d1, e1 = Polygon(C, F_{ba}, P_a)
f1 = OrthogonalLine(P_b, e)
g1 = OrthogonalLine(P_b, f)
h1 = OrthogonalLine(P_b, d)
F_{ab} = Intersect(f1, e)
F_{bb} = Intersect(g1, f)
F_{cb} = Intersect(h1, d)
poly4, m1, n1, p1 = Polygon(C, F_{ab}, P_b)
poly5, q1, r1, s1 = Polygon(C, F_{ab}, F_{bb})
poly6, t1, a2, b2 = Polygon(A, F_{cb}, F_{bb})
poly7, c2, d2, e2 = Polygon(A, F_{cb}, P_b)
poly8, f2, g2, h2 = Polygon(B, F_{ca}, F_{aa})
poly9, i2, j2, l2 = Polygon(B, F_{ca}, P_a)
p2 = Circle(P_a, F_{aa}, F_{ca})
q2 = Circle(P_a, F_{ba}, F_{aa})
P_c = Intersect(k2, l1)
m2 = OrthogonalLine(P_c, e)
n2 = OrthogonalLine(P_c, f)
r2 = OrthogonalLine(P_c, d)
F_{ac} = Intersect(m2, e)
F_{bc} = Intersect(n2, f)
F_{cc} = Intersect(r2, d)
poly10, s2, t2, a3 = Polygon(B, F_{cc}, F_{ac})
poly11, b3, c3, d3 = Polygon(B, P_c, F_{ac})
poly12, e3, f3, g3 = Polygon(A, F_{cc}, F_{bc})
poly13, h3, i3, j3 = Polygon(A, P_c, F_{bc})
p3 = Circle(P_c, F_{ac}, F_{cc})
q3 = Circle(P_c, F_{cc}, F_{bc})