construc R

A' symétrique de A / (BC) etc
A'' triangle BCA'' équilatéral direct etc
R = ∩ A'A'', B'B'', C'C''

A = (-3, 3)
B = (1.8621648462787737, 3.0695001467595597)
C = (-2.0772392217780755, 7.205296792989326)
c = Segment(A, B)
a = Segment(B, C)
b = Segment(C, A)
C' = Mirror(C, c)
A' = Mirror(A, a)
B' = Mirror(B, b)
C'' = Rotate(B, 60°, A)
cc = Line(C'', C')
A'' = Rotate(C, 60°, B)
aa = Line(A'', A')
B'' = Rotate(A, 60°, C)
bb = Line(B', B'')
R = Intersect(bb, aa)
f = Segment(C, B'')
g = Segment(B'', A)
h = Segment(C'', A)
i = Segment(C'', B)
j = Segment(C, A'')
k = Segment(A'', B)
l = Segment(C, C')
m = Segment(A', A)
n = Segment(B, B')
d = false
bc = Line(C, B)
ac = Line(A, C)
ab = Line(A, B)
p = OrthogonalLine(R, bc)
q = OrthogonalLine(R, ab)
r = OrthogonalLine(R, ac)
U = Intersect(p, bc)
V = Intersect(r, ac)
W = Intersect(q, ab)
s = Segment(R, U)
t = Segment(R, W)
e = Segment(R, V)
t1, w, u, v = Polygon(U, V, W)
c_1 = Circle(R, A)
P = Point(c_1)
f_1 = Ray(R, P)
PP: P
U' = Intersect(f_1, bc)
g_1 = Ray(R, Rotate[P, Angle[U, R, V], R])
h_1 = Ray(R, Rotate[P, Angle[U, R, W], R])
V' = Intersect(g_1, ac)
W' = Intersect(h_1, ab)
i_1 = Segment(V', U')
j_1 = Segment(U', W')
k_1 = Segment(W', V')