A = (0.54, 2.56)
B = (-0.92, -0.34)
C = (2.5, 0.04)
D = (6.68, 0.48)
E = (4.594693608951668, -2.280267118211463)
F = (8.525301697623675, -2.5910593856878537)
O = TriangleCenter(A, B, C, 3)
H = TriangleCenter(D, E, F, 3)
a: Distance[A, O] / Distance[D, H]
f(z) = (a * (z - H)) + O
D'_{1}: f(D)
E'_{1}: f(E)
F'_{1}: f(F)
g = Line(A, D'_{1})
h = Line(B, E'_{1})
i = Line(F'_{1}, C)
P_{1}: (2 * O) - D'_{1}
Q: (2 * O) - E'_{1}
R: (2 * O) - F'_{1}
k = Line(P_{1}, A)
j = Line(R, C)
l = Line(B, Q)
B' = Intersect(k, j)
C' = Intersect(k, l)
C'' = Intersect(g, h)
B'' = Intersect(g, i)
c = Circle(A, B', B'')
d = Circle(A, C'', C')
P = Intersect(c, d, 2)
e = Circle(O, A)
m = Line(A, P)
n = Line(B, P)
p = Line(P, C)
D' = Intersect(e, m, 2)
E' = Intersect(e, n, 2)
F' = Intersect(e, p, 1)
α = Angle(E', D', F')
β = Angle(E, D, F)
q = Segment(A, P)
r = Segment(P, D')
s = Segment(B, P)
t = Segment(P, E')
b = Segment(F', P)
f_1 = Segment(P, C)
g_1 = Segment(E, D)
h_1 = Segment(D, F)
i_1 = Segment(F, E)