Reflecting twice
Author: R. Albers

Change with the slider the angle α. Observe the angle γ.

A = (8.5, -3.74)
B = (10.42, -2.5800000000000027)
C = (9.52, 0.6799999999999999)
poly1, c, a, b = Polygon(A, B, C)
D = (5.66, -5.9)
E = (9.08, 2.16)
d = Line(D, E)
A' = Mirror(A, d)
B' = Mirror(B, d)
C' = Mirror(C, d)
poly1', c', a', b' = Polygon(A', B', C')
α = 0.7330382858376184 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
F = Rotate(E, α, D)
e = Line(D, F)
A'' = Mirror(A', e)
B'' = Mirror(B', e)
C'' = Mirror(C', e)
poly1'', c'', a'', b'' = Polygon(A'', B'', C'')
β = Angle(E, D, F)
h = Segment(A', D)
G = (7.185825332164527, -5.1093195335577715)
k = Circle(D, G)
H = Point(k)
f = Segment(H, D)
g = Segment(D, G)
γ = Angle(G, D, H)
p = CircleArc(D, G, H)