P = X(3608)

P = X(66622)

P = X(66623)

First Morley

Second Morley

Third Morley

A: (342549133 / 30368338, sqrt(68143844781297815) / 30368338)
B: (0, 0)
C: (197 / 13, 0)
a = Segment(B, C)
b = Segment(C, A)
c = Segment(A, B)
AB = Line(A, B)
BC = Line(B, C)
CA = Line(C, A)
aa: acosd(((-a^(2)) + b^(2) + c^(2)) / (((2 * b) * c)))
bb: acosd((a^(2) - b^(2) + c^(2)) / (((2 * a) * c)))
cc: acosd((a^(2) + b^(2) - c^(2)) / (((2 * a) * b)))
Morley = 1 (slider from 1 to 3, step 1)
ma = Barycenter({A, B, C}, {sin(aa), ((2 * cos(cc / 3 + ((2 / 3 * (1 + Morley / 2 + ((3 * Morley^(2))) / 2)) * pi))) * sin(bb)), ((2 * cos(bb / 3 + ((2 / 3 * (1 + Morley / 2 + ((3 * Morley^(2))) / 2)) * pi))) * sin(cc))})
mb = Barycenter({A, B, C}, {((2 * cos(cc / 3 + ((2 / 3 * (1 + Morley / 2 + ((3 * Morley^(2))) / 2)) * pi))) * sin(aa)), sin(bb), ((2 * cos(aa / 3 + ((2 / 3 * (1 + Morley / 2 + ((3 * Morley^(2))) / 2)) * pi))) * sin(cc))})
mc = Barycenter({A, B, C}, {((2 * cos(bb / 3 + ((2 / 3 * (1 + Morley / 2 + ((3 * Morley^(2))) / 2)) * pi))) * sin(aa)), ((2 * cos(aa / 3 + ((2 / 3 * (1 + Morley / 2 + ((3 * Morley^(2))) / 2)) * pi))) * sin(bb)), sin(cc)})
f = Segment(mb, mc)
g = Segment(mc, ma)
h = Segment(ma, mb)
s1 = Barycenter({A, B, C}, {(((3 * cos((bb - cc) / 3)) + cos(bb - cc)) * sin(aa)), ((cos(aa - cc) - (3 * cos((1 / 3 * (bb + (2 * cc)))))) * sin(bb)), ((cos(aa - bb) - (3 * cos((1 / 3 * ((2 * bb) + cc))))) * sin(cc))})
s2 = Barycenter({A, B, C}, {((cos(bb - cc) - (3 * cos((1 / 3 * (aa + (2 * cc)))))) * sin(aa)), ((cos(aa - cc) + (3 * cos((1 / 3 * ((-aa) + cc))))) * sin(bb)), ((cos(aa - bb) - (3 * cos((1 / 3 * ((2 * aa) + cc))))) * sin(cc))})
s3 = Barycenter({A, B, C}, {(((-3 * cos((1 / 3 * (aa + (2 * bb))))) + cos(bb - cc)) * sin(aa)), (((-3 * cos((1 / 3 * ((2 * aa) + bb)))) + cos(aa - cc)) * sin(bb)), (((3 * cos((aa - bb) / 3)) + cos(aa - bb)) * sin(cc))})
x5 = TriangleCenter(A, B, C, 5)
x3 = TriangleCenter(A, B, C, 3)
e = Circle(x3, A)
Q = Point(e)
tP = OrthogonalLine(Q, Line[x3, Q])
D = Intersect(tP, OrthogonalLine[A, tP])
E = Intersect(tP, OrthogonalLine[B, tP])
F = Intersect(tP, OrthogonalLine[C, tP])
i = OrthogonalLine(D, BC)
j = OrthogonalLine(E, CA)
k = OrthogonalLine(F, AB)
G = Intersect(k, j)
loc1 = Locus(G, Q)
l = Line(s1, ma)
m = Line(s2, mb)
n = Line(s3, mc)
P = Intersect(m, n)