A = (0, 0)
B = (0, 1)
C = (0.8660254037844386, 0.5)
poly1, c, a, b = Polygon(A, B, C)
D = Midpoint(c)
A' = Rotate(A, 180°, D)
B' = Rotate(B, 180°, D)
C' = Rotate(C, 180°, D)
poly1', c', a', b' = Polygon(A', B', C')
f = Line(B, b)
g = Line(B, a)
h = Line(C, c)
E = Intersect(f, h)
i = Line(C, f)
j = Line(C', a')
k = Line(A, c)
l = Line(E, j)
F = Intersect(h, j)
G = Intersect(k, l)
m = Line(G, f)
n = Line(F, i)
H = Intersect(k, n)
p = Line(H, j)
I = Intersect(i, p)
J = Intersect(f, p)
K = Intersect(m, p)
L = Intersect(j, m)
M = Intersect(g, m)
N = Intersect(i, l)
O = Intersect(l, n)
P = Intersect(g, n)
q = Line(I, k)
r_1 = Line(J, q)
s = Line(K, r_1)
t = Line(N, h)
d = Line(O, t)
e = AngularBisector(C, B, A)
f_1 = AngularBisector(B, A, C)
Q = Intersect(e, f_1)
g_1 = OrthogonalLine(Q, k)
R = Intersect(k, g_1)
c_1 = Circle(Q, R)
max = Segment(Q, R)
r = 0.14 (slider from 0 to max, step 0.001)
S = PointIn(poly1)
d_1 = Circle(S, r)
T, W = Intersect(d_1, k)
U, Z = Intersect(d_1, i)
V, A_1 = Intersect(d_1, g)
tracer: (x(S), y(S))
touchLine = If((x(T) > -100) ∨ (x(A_1) > -100) ∨ (x(Z) > -100), true, false)
e_1 = Circle(A, r)
h_1 = OrthogonalLine(A, k)
B_1 = Intersect(e_1, h_1, 1)
i_1 = Line(B_1, k)
C_1 = Intersect(f_1, i_1)
D_1 = Intersect(e, i_1)
j_1 = AngularBisector(A, C, B)
k_1 = Circle(C, r)
l_1 = OrthogonalLine(C, i)
E_1 = Intersect(k_1, l_1, 1)
m_1 = Line(E_1, i)
F_1 = Intersect(j_1, m_1)
n_1 = Line(D_1, F_1)
poly2, f_2, c_2, d_2 = Polygon(C_1, D_1, F_1)
o: Area[poly2] / Area[poly1]
text1: "" + (LaTeX[poly2]) + "/" + (LaTeX[poly1]) + " ≈" + (LaTeX[o]) + ""
u = Area(poly2)
v = Area(poly1)