show equiangular points locus

A = Intersect(xAxis, yAxis)
B = Point(xAxis)
C = (1.0695421487603347, 3.746955371900838)
t1, c, a, b = Polygon(A, B, C)
α = 0 rad (slider from 0 to 360°)
f = LineBisector(A, C)
C' = Rotate(C, 90° - α / 2, A)
g = Line(A, C')
D = Intersect(f, g)
d = Circle(D, A)
C_1 = Rotate(C, -90° + α / 2, B)
h = LineBisector(B, C)
i = Line(B, C_1)
E = Intersect(h, i)
e = Circle(E, C)
F, G = Intersect(d, e)
loc1 = Locus(F, α)
loc2 = Locus(G, α)
k = false
P = (2.52408760330579, 0.9535669421487734)
l = Segment(P, C)
m = Segment(P, B)
n = Segment(P, A)
t: l + m + n
text1: "PA+PB+PC=" + (LaTeX[t]) + ""
β = Angle(A, P, B)