A = (11.7233080340107, 8.94268624609277)
B = (0.43296642382008343, 0)
C = (15, 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)
S: (1 / 2 * sqrt(((((a + b - c) * (a - b + c)) * ((-a) + b + c)) * (a + b + c))))
J: sqrt(a^(6) - (a^(4) * b^(2)) - (a^(2) * b^(4)) + b^(6) - (a^(4) * c^(2)) + (((3 * a^(2)) * b^(2)) * c^(2)) - (b^(4) * c^(2)) - (a^(2) * c^(4)) - (b^(2) * c^(4)) + c^(6)) / (((a * b) * c))
cc = Circle(A, B, C)
P = Point(cc)
X3 = TriangleCenter(A, B, C, 3)
X2 = TriangleCenter(A, B, C, 2)
P' = Mirror(P, X3)
Q = Midpoint(P, X2)
Q' = Midpoint(P', X2)
D = TriangleCenter(P, Q, P', 4)
e = Conic(P, P', Q, Q', D)
f = Line(X3, X2)
E1 = Barycenter({A, B, C}, {((((a * b) * c) * ((2 * a^(4)) - (a^(2) * b^(2)) - b^(4) - (a^(2) * c^(2)) + ((2 * b^(2)) * c^(2)) - c^(4))) * sqrt(((((-a^(2)) - b^(2) - c^(2)) * (-9 + J)) * (9 + J)))) - ((2 * ((10 * a^(6)) - (a^(4) * b^(2)) - ((10 * a^(2)) * b^(4)) + b^(6) - (a^(4) * c^(2)) + (((12 * a^(2)) * b^(2)) * c^(2)) - (b^(4) * c^(2)) - ((10 * a^(2)) * c^(4)) - (b^(2) * c^(4)) + c^(6))) * S), ((((a * b) * c) * ((-a^(4)) - (a^(2) * b^(2)) + (2 * b^(4)) + ((2 * a^(2)) * c^(2)) - (b^(2) * c^(2)) - c^(4))) * sqrt(((((-a^(2)) - b^(2) - c^(2)) * (-9 + J)) * (9 + J)))) - ((2 * (a^(6) - ((10 * a^(4)) * b^(2)) - (a^(2) * b^(4)) + (10 * b^(6)) - (a^(4) * c^(2)) + (((12 * a^(2)) * b^(2)) * c^(2)) - (b^(4) * c^(2)) - (a^(2) * c^(4)) - ((10 * b^(2)) * c^(4)) + c^(6))) * S), ((((a * b) * c) * ((-a^(4)) + ((2 * a^(2)) * b^(2)) - b^(4) - (a^(2) * c^(2)) - (b^(2) * c^(2)) + (2 * c^(4)))) * sqrt(((((-a^(2)) - b^(2) - c^(2)) * (-9 + J)) * (9 + J)))) - ((2 * (a^(6) - (a^(4) * b^(2)) - (a^(2) * b^(4)) + b^(6) - ((10 * a^(4)) * c^(2)) + (((12 * a^(2)) * b^(2)) * c^(2)) - ((10 * b^(4)) * c^(2)) - (a^(2) * c^(4)) - (b^(2) * c^(4)) + (10 * c^(6)))) * S)})
E2 = Barycenter({A, B, C}, {((((a * b) * c) * ((2 * a^(4)) - (a^(2) * b^(2)) - b^(4) - (a^(2) * c^(2)) + ((2 * b^(2)) * c^(2)) - c^(4))) * sqrt(((((-a^(2)) - b^(2) - c^(2)) * (-9 + J)) * (9 + J)))) + ((2 * ((10 * a^(6)) - (a^(4) * b^(2)) - ((10 * a^(2)) * b^(4)) + b^(6) - (a^(4) * c^(2)) + (((12 * a^(2)) * b^(2)) * c^(2)) - (b^(4) * c^(2)) - ((10 * a^(2)) * c^(4)) - (b^(2) * c^(4)) + c^(6))) * S), ((((a * b) * c) * ((-a^(4)) - (a^(2) * b^(2)) + (2 * b^(4)) + ((2 * a^(2)) * c^(2)) - (b^(2) * c^(2)) - c^(4))) * sqrt(((((-a^(2)) - b^(2) - c^(2)) * (-9 + J)) * (9 + J)))) + ((2 * (a^(6) - ((10 * a^(4)) * b^(2)) - (a^(2) * b^(4)) + (10 * b^(6)) - (a^(4) * c^(2)) + (((12 * a^(2)) * b^(2)) * c^(2)) - (b^(4) * c^(2)) - (a^(2) * c^(4)) - ((10 * b^(2)) * c^(4)) + c^(6))) * S), ((((a * b) * c) * ((-a^(4)) + ((2 * a^(2)) * b^(2)) - b^(4) - (a^(2) * c^(2)) - (b^(2) * c^(2)) + (2 * c^(4)))) * sqrt(((((-a^(2)) - b^(2) - c^(2)) * (-9 + J)) * (9 + J)))) + ((2 * (a^(6) - (a^(4) * b^(2)) - (a^(2) * b^(4)) + b^(6) - ((10 * a^(4)) * c^(2)) + (((12 * a^(2)) * b^(2)) * c^(2)) - ((10 * b^(4)) * c^(2)) - (a^(2) * c^(4)) - (b^(2) * c^(4)) + (10 * c^(6)))) * S)})
X37904 = Midpoint(E1, E2)
g = FirstAxis(e)
k = OrthogonalLine(X37904, g)