A = (12.474546433821686, 7.201959804231775)
B: (0, 0)
c = Segment(A, B)
C: (197 / 13, 0)
b = Segment(C, A)
a = Segment(B, C)
cubicEqn = TriangleCurve(A, B, C, 0 = (((((a^(2) * b^(2)) * B^(3)) * (a - c)) * c^(2)) * (a + c)) - (((((a^(2) * A^(3)) * b^(2)) * (b - c)) * c^(2)) * (b + c)) + (((A * B^(2)) * c^(2)) * (a^(6) - (a^(4) * c^(2)) - ((a^(2) * b^(2)) * c^(2)) + (b^(4) * c^(2)) + (a^(2) * c^(4)) - c^(6))) - (((A^(2) * B) * c^(2)) * (b^(6) + (a^(4) * c^(2)) - ((a^(2) * b^(2)) * c^(2)) - (b^(4) * c^(2)) + (b^(2) * c^(4)) - c^(6))) + ((((((((((2 * A) * (a - b)) * (a + b)) * B) * (a - c)) * (b - c)) * (a + c)) * (b + c)) * (a^(2) + b^(2) + c^(2))) * C) + (((a^(2) * B^(2)) * (a^(6) - (a^(2) * b^(4)) - (a^(4) * c^(2)) + ((a^(2) * b^(2)) * c^(2)) + (a^(2) * c^(4)) - c^(6))) * C) + (((A^(2) * b^(2)) * ((a^(4) * b^(2)) - b^(6) - ((a^(2) * b^(2)) * c^(2)) + (b^(4) * c^(2)) - (b^(2) * c^(4)) + c^(6))) * C) - (((a^(2) * B) * (a^(6) - (a^(4) * b^(2)) + (a^(2) * b^(4)) - b^(6) + ((a^(2) * b^(2)) * c^(2)) - (a^(2) * c^(4)))) * C^(2)) - (((A * b^(2)) * (a^(6) - (a^(4) * b^(2)) + (a^(2) * b^(4)) - b^(6) - ((a^(2) * b^(2)) * c^(2)) + (b^(2) * c^(4)))) * C^(2)) - (((((a^(2) * (a - b)) * b^(2)) * (a + b)) * c^(2)) * C^(3)))
MoveMe = Point(cubicEqn)
AB = Line(A, B)
BC = Line(B, C)
CA = Line(C, A)
barysP = Element(Transpose[ReducedRowEchelonForm[{{x(A), x(B), x(C), x(MoveMe)}, {y(A), y(B), y(C), y(MoveMe)}, {1, 1, 1, 1}}]], 4)
CIP = Barycenter({A, B, C}, {((((barysP(1) * (barysP(1) + barysP(2) + barysP(3))) * a^(2)) * b^(2)) * c^(2)) + ((a^(2) * ((-a^(2)) + b^(2) + c^(2))) * (((barysP(2) * barysP(3)) * a^(2)) + ((barysP(1) * barysP(3)) * b^(2)) + ((barysP(1) * barysP(2)) * c^(2)))), ((((barysP(2) * (barysP(1) + barysP(2) + barysP(3))) * a^(2)) * b^(2)) * c^(2)) + ((b^(2) * (a^(2) - b^(2) + c^(2))) * (((barysP(2) * barysP(3)) * a^(2)) + ((barysP(1) * barysP(3)) * b^(2)) + ((barysP(1) * barysP(2)) * c^(2)))), ((((barysP(3) * (barysP(1) + barysP(2) + barysP(3))) * a^(2)) * b^(2)) * c^(2)) + ((c^(2) * (a^(2) + b^(2) - c^(2))) * (((barysP(2) * barysP(3)) * a^(2)) + ((barysP(1) * barysP(3)) * b^(2)) + ((barysP(1) * barysP(2)) * c^(2))))})
x3 = TriangleCenter(A, B, C, 3)
x2 = TriangleCenter(A, B, C, 2)
x39 = TriangleCenter(A, B, C, 39)
x114 = TriangleCenter(A, B, C, 114)
x1125 = TriangleCenter(A, B, C, 1125)
mKiepert = Conic(x2, x3, x39, x114, x1125)