X14121

sg = 1 (slider from -1 to 1, step 2)
C: (197 / 13, 0)
B: (0, 0)
a = Segment(B, C)
A: (342549133 / 30368338, sqrt(68143844781297815) / 30368338)
c = Segment(A, B)
b = Segment(C, A)
AB = Line(A, B)
BC = Line(B, C)
CA = Line(C, A)
S: (sg / 2 * sqrt(((((a + b - c) * (a - b + c)) * ((-a) + b + c)) * (a + b + c))))
ca = Barycenter({A, B, C}, {((a * ((-a) + b + c)) * (a + b + c)) + ((2 * (b + c)) * S), (b * ((((-a) + b + c) * (a + b + c)) - (2 * S))), (c * ((((-a) + b + c) * (a + b + c)) - (2 * S)))})
cb = Barycenter({A, B, C}, {(a * (((a - b + c) * (a + b + c)) - (2 * S))), ((b * (a - b + c)) * (a + b + c)) + ((2 * (a + c)) * S), (c * (((a - b + c) * (a + b + c)) - (2 * S)))})
cc = Barycenter({A, B, C}, {(a * (((a + b - c) * (a + b + c)) - (2 * S))), (b * (((a + b - c) * (a + b + c)) - (2 * S))), (((a + b - c) * c) * (a + b + c)) + ((2 * (a + b)) * S)})
d = Circle(ca, Intersect[Line[A, B], OrthogonalLine[ca, Line[A, B]]])
e = Circle(cb, Intersect[Line[B, C], OrthogonalLine[cb, Line[B, C]]])
f = Circle(cc, Intersect[Line[C, A], OrthogonalLine[cc, Line[C, A]]])
g = Circle(Midpoint[B, C], B)
h = Circle(Midpoint[C, A], A)
k_{1} = Circle(Midpoint[A, B], B)
i = Line(A, c)
H = Barycenter({A, B, C}, {((-a) * (b + c)), (a * b) + S, (a * c) + S})
tc = Barycenter({A, B, C}, {(((a * c) + S) * ((((-a) - b + c) * (a + b + c)) + (2 * S))), (((b * c) + S) * ((((-a) - b + c) * (a + b + c)) + (2 * S))), (c * (((c * ((-a) - b + c)) * (a + b + c)) - ((2 * (a + b)) * S)))})
tb = Barycenter({A, B, C}, {(((a * b) + S) * ((((-a) + b - c) * (a + b + c)) + (2 * S))), (b * (((b * ((-a) + b - c)) * (a + b + c)) - ((2 * (a + c)) * S))), (((b * c) + S) * ((((-a) + b - c) * (a + b + c)) + (2 * S)))})
ta = Barycenter({A, B, C}, {(a * (((a * (a - b - c)) * (a + b + c)) - ((2 * (b + c)) * S))), (((a * b) + S) * (((a - b - c) * (a + b + c)) + (2 * S))), (((a * c) + S) * (((a - b - c) * (a + b + c)) + (2 * S)))})
sa = Barycenter({A, B, C}, {0, (((-a) - b + c) * (a + b + c)) + (2 * S), ((a - b + c) * (a + b + c)) - (2 * S)})
sb = Barycenter({A, B, C}, {((a + b - c) * (a + b + c)) - (2 * S), 0, ((a - b - c) * (a + b + c)) + (2 * S)})
sc = Barycenter({A, B, C}, {(((-a) + b - c) * (a + b + c)) + (2 * S), (((-a) + b + c) * (a + b + c)) - (2 * S), 0})
j = Line(sc, sb)
oa = Intersect(j, OrthogonalLine[ca, j])
x7 = TriangleCenter(A, B, C, 7)
voa = Mirror(oa, d)
l = Line(x7, voa)
tAi = Barycenter({A, B, C}, {((-4 * a) * S), ((a + b - c) * (((a - b - c) * (a + b + c)) + (2 * S))), ((a - b + c) * (((a - b - c) * (a + b + c)) + (2 * S)))})
tBi = Barycenter({A, B, C}, {((a + b - c) * ((((-a) + b - c) * (a + b + c)) + (2 * S))), ((-4 * b) * S), (((-a) + b + c) * ((((-a) + b - c) * (a + b + c)) + (2 * S)))})
tCi = Barycenter({A, B, C}, {((a - b + c) * ((((-a) - b + c) * (a + b + c)) + (2 * S))), (((-a) + b + c) * ((((-a) - b + c) * (a + b + c)) + (2 * S))), ((-4 * c) * S)})
p = Circle(tAi, tBi, tCi)
cI = TriangleCenter(tAi, tBi, tCi, 3)
tAe = Barycenter({A, B, C}, {(-4 * ((((a + b - c) * (a - b + c)) * (a + b + c)) + (a * S))), ((a + b - c) * (((a - b - c) * (a + b + c)) + (2 * S))), ((a - b + c) * (((a - b - c) * (a + b + c)) + (2 * S)))})
tBe = Barycenter({A, B, C}, {((a + b - c) * ((((-a) + b - c) * (a + b + c)) + (2 * S))), (-4 * ((((a + b - c) * ((-a) + b + c)) * (a + b + c)) + (b * S))), (((-a) + b + c) * ((((-a) + b - c) * (a + b + c)) + (2 * S)))})
tCe = Barycenter({A, B, C}, {((a - b + c) * ((((-a) - b + c) * (a + b + c)) + (2 * S))), (((-a) + b + c) * ((((-a) - b + c) * (a + b + c)) + (2 * S))), (-4 * ((((a - b + c) * ((-a) + b + c)) * (a + b + c)) + (c * S)))})
q = Circle(tAe, tBe, tCe)
cE = TriangleCenter(tAe, tBe, tCe, 3)
x1 = TriangleCenter(A, B, C, 1)
m = Line(x1, x7)
tAim = Barycenter({A, B, C}, {((2 * a) * ((((a - b - c)^(2) * (b - c)^(2)) * (a + b + c)) - ((2 * (a^(3) - b^(3) + (b^(2) * c) + (b * c^(2)) - c^(3))) * S))), (((a - b - c) * (a + b + c)) * (a^(4) - (a^(3) * b) - (a^(2) * b^(2)) - (a * b^(3)) + (2 * b^(4)) + (a^(3) * c) + (((4 * a^(2)) * b) * c) + ((a * b^(2)) * c) - ((4 * b^(3)) * c) - ((3 * a^(2)) * c^(2)) + ((a * b) * c^(2)) + ((4 * b^(2)) * c^(2)) - (a * c^(3)) - ((4 * b) * c^(3)) + (2 * c^(4)))) + (((2 * a) * (a^(3) + (a^(2) * b) + (a * b^(2)) - (3 * b^(3)) - (a^(2) * c) + ((3 * b^(2)) * c) - (a * c^(2)) - (b * c^(2)) + c^(3))) * S), (((a - b - c) * (a + b + c)) * (a^(4) + (a^(3) * b) - ((3 * a^(2)) * b^(2)) - (a * b^(3)) + (2 * b^(4)) - (a^(3) * c) + (((4 * a^(2)) * b) * c) + ((a * b^(2)) * c) - ((4 * b^(3)) * c) - (a^(2) * c^(2)) + ((a * b) * c^(2)) + ((4 * b^(2)) * c^(2)) - (a * c^(3)) - ((4 * b) * c^(3)) + (2 * c^(4)))) + (((2 * a) * (a^(3) - (a^(2) * b) - (a * b^(2)) + b^(3) + (a^(2) * c) - (b^(2) * c) + (a * c^(2)) + ((3 * b) * c^(2)) - (3 * c^(3)))) * S)})
tBim = Barycenter({A, B, C}, {((((-a) + b - c) * (a + b + c)) * ((2 * a^(4)) - (a^(3) * b) - (a^(2) * b^(2)) - (a * b^(3)) + b^(4) - ((4 * a^(3)) * c) + ((a^(2) * b) * c) + (((4 * a) * b^(2)) * c) + (b^(3) * c) + ((4 * a^(2)) * c^(2)) + ((a * b) * c^(2)) - ((3 * b^(2)) * c^(2)) - ((4 * a) * c^(3)) - (b * c^(3)) + (2 * c^(4)))) + (((2 * b) * ((-3 * a^(3)) + (a^(2) * b) + (a * b^(2)) + b^(3) + ((3 * a^(2)) * c) - (b^(2) * c) - (a * c^(2)) - (b * c^(2)) + c^(3))) * S), ((2 * b) * (((((-a) + b - c)^(2) * ((-a) + c)^(2)) * (a + b + c)) - ((2 * ((-a^(3)) + b^(3) + (a^(2) * c) + (a * c^(2)) - c^(3))) * S))), ((((-a) + b - c) * (a + b + c)) * ((2 * a^(4)) - (a^(3) * b) - ((3 * a^(2)) * b^(2)) + (a * b^(3)) + b^(4) - ((4 * a^(3)) * c) + ((a^(2) * b) * c) + (((4 * a) * b^(2)) * c) - (b^(3) * c) + ((4 * a^(2)) * c^(2)) + ((a * b) * c^(2)) - (b^(2) * c^(2)) - ((4 * a) * c^(3)) - (b * c^(3)) + (2 * c^(4)))) + (((2 * b) * (a^(3) - (a^(2) * b) - (a * b^(2)) + b^(3) - (a^(2) * c) + (b^(2) * c) + ((3 * a) * c^(2)) + (b * c^(2)) - (3 * c^(3)))) * S)})
tCim = Barycenter({A, B, C}, {((((-a) - b + c) * (a + b + c)) * ((2 * a^(4)) - ((4 * a^(3)) * b) + ((4 * a^(2)) * b^(2)) - ((4 * a) * b^(3)) + (2 * b^(4)) - (a^(3) * c) + ((a^(2) * b) * c) + ((a * b^(2)) * c) - (b^(3) * c) - (a^(2) * c^(2)) + (((4 * a) * b) * c^(2)) - ((3 * b^(2)) * c^(2)) - (a * c^(3)) + (b * c^(3)) + c^(4))) + (((2 * c) * ((-3 * a^(3)) + ((3 * a^(2)) * b) - (a * b^(2)) + b^(3) + (a^(2) * c) - (b^(2) * c) + (a * c^(2)) - (b * c^(2)) + c^(3))) * S), ((((-a) - b + c) * (a + b + c)) * ((2 * a^(4)) - ((4 * a^(3)) * b) + ((4 * a^(2)) * b^(2)) - ((4 * a) * b^(3)) + (2 * b^(4)) - (a^(3) * c) + ((a^(2) * b) * c) + ((a * b^(2)) * c) - (b^(3) * c) - ((3 * a^(2)) * c^(2)) + (((4 * a) * b) * c^(2)) - (b^(2) * c^(2)) + (a * c^(3)) - (b * c^(3)) + c^(4))) + (((2 * c) * (a^(3) - (a^(2) * b) + ((3 * a) * b^(2)) - (3 * b^(3)) - (a^(2) * c) + (b^(2) * c) - (a * c^(2)) + (b * c^(2)) + c^(3))) * S), ((2 * c) * ((((a - b)^(2) * ((-a) - b + c)^(2)) * (a + b + c)) - ((2 * ((-a^(3)) + (a^(2) * b) + (a * b^(2)) - b^(3) + c^(3))) * S)))})
t = Circle(tAim, tBim, tCim)
x14121 = Barycenter({A, B, C}, {(((a - b - c) * (a + b + c)) * ((2 * a^(4)) - (a^(3) * b) - (a^(2) * b^(2)) + (a * b^(3)) - b^(4) - (a^(3) * c) + (((2 * a^(2)) * b) * c) - ((a * b^(2)) * c) - (a^(2) * c^(2)) - ((a * b) * c^(2)) + ((2 * b^(2)) * c^(2)) + (a * c^(3)) - c^(4))) - ((2 * (a^(4) - (a^(3) * b) + (a^(2) * b^(2)) + (a * b^(3)) - (2 * b^(4)) - (a^(3) * c) + (((2 * a^(2)) * b) * c) - ((a * b^(2)) * c) + (a^(2) * c^(2)) - ((a * b) * c^(2)) + ((4 * b^(2)) * c^(2)) + (a * c^(3)) - (2 * c^(4)))) * S), ((((-a) + b - c) * (a + b + c)) * ((-a^(4)) + (a^(3) * b) - (a^(2) * b^(2)) - (a * b^(3)) + (2 * b^(4)) - ((a^(2) * b) * c) + (((2 * a) * b^(2)) * c) - (b^(3) * c) + ((2 * a^(2)) * c^(2)) - ((a * b) * c^(2)) - (b^(2) * c^(2)) + (b * c^(3)) - c^(4))) - ((2 * ((-2 * a^(4)) + (a^(3) * b) + (a^(2) * b^(2)) - (a * b^(3)) + b^(4) - ((a^(2) * b) * c) + (((2 * a) * b^(2)) * c) - (b^(3) * c) + ((4 * a^(2)) * c^(2)) - ((a * b) * c^(2)) + (b^(2) * c^(2)) + (b * c^(3)) - (2 * c^(4)))) * S), ((((-a) - b + c) * (a + b + c)) * ((-a^(4)) + ((2 * a^(2)) * b^(2)) - b^(4) + (a^(3) * c) - ((a^(2) * b) * c) - ((a * b^(2)) * c) + (b^(3) * c) - (a^(2) * c^(2)) + (((2 * a) * b) * c^(2)) - (b^(2) * c^(2)) - (a * c^(3)) - (b * c^(3)) + (2 * c^(4)))) - ((2 * ((-2 * a^(4)) + ((4 * a^(2)) * b^(2)) - (2 * b^(4)) + (a^(3) * c) - ((a^(2) * b) * c) - ((a * b^(2)) * c) + (b^(3) * c) + (a^(2) * c^(2)) + (((2 * a) * b) * c^(2)) + (b^(2) * c^(2)) - (a * c^(3)) - (b * c^(3)) + c^(4))) * S)})
T = Barycenter({A, B, C}, {(((2 * a^(5)) - ((2 * a^(4)) * b) + (a^(3) * b^(2)) - (a^(2) * b^(3)) + (a * b^(4)) - b^(5) - ((2 * a^(4)) * c) + ((a^(2) * b^(2)) * c) + (b^(4) * c) + (a^(3) * c^(2)) + ((a^(2) * b) * c^(2)) - (((2 * a) * b^(2)) * c^(2)) - (a^(2) * c^(3)) + (a * c^(4)) + (b * c^(4)) - c^(5)) * (a^(5) - (a^(4) * b) - (a * b^(4)) + b^(5) - (a^(4) * c) + ((a^(3) * b) * c) + ((a * b^(3)) * c) - (b^(4) * c) + ((a * b) * c^(3)) - (a * c^(4)) - (b * c^(4)) + c^(5))) + (((2 * (b - c)^(2)) * (a^(6) - ((2 * a^(5)) * b) + ((3 * a^(4)) * b^(2)) - ((4 * a^(3)) * b^(3)) + ((3 * a^(2)) * b^(4)) - ((2 * a) * b^(5)) + b^(6) - ((2 * a^(5)) * c) + (((5 * a^(4)) * b) * c) - (((5 * a^(3)) * b^(2)) * c) + (((3 * a^(2)) * b^(3)) * c) - ((a * b^(4)) * c) + ((3 * a^(4)) * c^(2)) - (((5 * a^(3)) * b) * c^(2)) + (((2 * a^(2)) * b^(2)) * c^(2)) + ((a * b^(3)) * c^(2)) - (b^(4) * c^(2)) - ((4 * a^(3)) * c^(3)) + (((3 * a^(2)) * b) * c^(3)) + ((a * b^(2)) * c^(3)) + ((3 * a^(2)) * c^(4)) - ((a * b) * c^(4)) - (b^(2) * c^(4)) - ((2 * a) * c^(5)) + c^(6))) * S), (((-a^(5)) + (a^(4) * b) - (a^(3) * b^(2)) + (a^(2) * b^(3)) - ((2 * a) * b^(4)) + (2 * b^(5)) + (a^(4) * c) + ((a^(2) * b^(2)) * c) - ((2 * b^(4)) * c) - (((2 * a^(2)) * b) * c^(2)) + ((a * b^(2)) * c^(2)) + (b^(3) * c^(2)) - (b^(2) * c^(3)) + (a * c^(4)) + (b * c^(4)) - c^(5)) * (a^(5) - (a^(4) * b) - (a * b^(4)) + b^(5) - (a^(4) * c) + ((a^(3) * b) * c) + ((a * b^(3)) * c) - (b^(4) * c) + ((a * b) * c^(3)) - (a * c^(4)) - (b * c^(4)) + c^(5))) + (((2 * ((-a) + c)^(2)) * (a^(6) - ((2 * a^(5)) * b) + ((3 * a^(4)) * b^(2)) - ((4 * a^(3)) * b^(3)) + ((3 * a^(2)) * b^(4)) - ((2 * a) * b^(5)) + b^(6) - ((a^(4) * b) * c) + (((3 * a^(3)) * b^(2)) * c) - (((5 * a^(2)) * b^(3)) * c) + (((5 * a) * b^(4)) * c) - ((2 * b^(5)) * c) - (a^(4) * c^(2)) + ((a^(3) * b) * c^(2)) + (((2 * a^(2)) * b^(2)) * c^(2)) - (((5 * a) * b^(3)) * c^(2)) + ((3 * b^(4)) * c^(2)) + ((a^(2) * b) * c^(3)) + (((3 * a) * b^(2)) * c^(3)) - ((4 * b^(3)) * c^(3)) - (a^(2) * c^(4)) - ((a * b) * c^(4)) + ((3 * b^(2)) * c^(4)) - ((2 * b) * c^(5)) + c^(6))) * S), ((a^(5) - (a^(4) * b) - (a * b^(4)) + b^(5) - (a^(4) * c) + ((a^(3) * b) * c) + ((a * b^(3)) * c) - (b^(4) * c) + ((a * b) * c^(3)) - (a * c^(4)) - (b * c^(4)) + c^(5)) * ((-a^(5)) + (a^(4) * b) + (a * b^(4)) - b^(5) + (a^(4) * c) - (((2 * a^(2)) * b^(2)) * c) + (b^(4) * c) - (a^(3) * c^(2)) + ((a^(2) * b) * c^(2)) + ((a * b^(2)) * c^(2)) - (b^(3) * c^(2)) + (a^(2) * c^(3)) + (b^(2) * c^(3)) - ((2 * a) * c^(4)) - ((2 * b) * c^(4)) + (2 * c^(5)))) + (((2 * (a - b)^(2)) * (a^(6) - (a^(4) * b^(2)) - (a^(2) * b^(4)) + b^(6) - ((2 * a^(5)) * c) - ((a^(4) * b) * c) + ((a^(3) * b^(2)) * c) + ((a^(2) * b^(3)) * c) - ((a * b^(4)) * c) - ((2 * b^(5)) * c) + ((3 * a^(4)) * c^(2)) + (((3 * a^(3)) * b) * c^(2)) + (((2 * a^(2)) * b^(2)) * c^(2)) + (((3 * a) * b^(3)) * c^(2)) + ((3 * b^(4)) * c^(2)) - ((4 * a^(3)) * c^(3)) - (((5 * a^(2)) * b) * c^(3)) - (((5 * a) * b^(2)) * c^(3)) - ((4 * b^(3)) * c^(3)) + ((3 * a^(2)) * c^(4)) + (((5 * a) * b) * c^(4)) + ((3 * b^(2)) * c^(4)) - ((2 * a) * c^(5)) - ((2 * b) * c^(5)) + c^(6))) * S)})
x218 = TriangleCenter(A, B, C, 218)
x4 = TriangleCenter(A, B, C, 4)
f_1 = Line(x4, x218)
g_1 = Line(cI, x14121)
K1051 = TriangleCurve(A, B, C, 0 = (((A^(2) * B) * (a^(2) - b^(2) + (b * c) - c^(2))) * (a^(3) - (a^(2) * b) - (a * b^(2)) + b^(3) - (a^(2) * c) + ((a * b) * c) + (a * c^(2)) - c^(3))) + (((A * B^(2)) * (a^(2) - b^(2) - (a * c) + c^(2))) * (a^(3) - (a^(2) * b) - (a * b^(2)) + b^(3) + ((a * b) * c) - (b^(2) * c) + (b * c^(2)) - c^(3))) + (((B^(2) * C) * (a^(2) - b^(2) - (a * c) + c^(2))) * (a^(3) - (a^(2) * b) + (a * b^(2)) - b^(3) - ((a * b) * c) + (b^(2) * c) + (b * c^(2)) - c^(3))) - (((B * C^(2)) * (a^(2) - (a * b) + b^(2) - c^(2))) * (a^(3) - b^(3) - (a^(2) * c) - ((a * b) * c) + (b^(2) * c) + (a * c^(2)) + (b * c^(2)) - c^(3))) - (((A^(2) * C) * (a^(2) - b^(2) + (b * c) - c^(2))) * (a^(3) - (a^(2) * b) + (a * b^(2)) - b^(3) - (a^(2) * c) + ((a * b) * c) - (a * c^(2)) + c^(3))) - (((A * C^(2)) * (a^(2) - (a * b) + b^(2) - c^(2))) * (a^(3) - b^(3) - (a^(2) * c) + ((a * b) * c) + (b^(2) * c) - (a * c^(2)) - (b * c^(2)) + c^(3))))
P1 = Intersect(j, m)
x10015 = Barycenter({A, B, C}, {((b - c) * (((-a^(2)) * b) + b^(3) - (a^(2) * c) + (((2 * a) * b) * c) - (b^(2) * c) - (b * c^(2)) + c^(3))), (((-a) + c) * (a^(3) - (a * b^(2)) - (a^(2) * c) + (((2 * a) * b) * c) - (b^(2) * c) - (a * c^(2)) + c^(3))), ((a - b) * (a^(3) - (a^(2) * b) - (a * b^(2)) + b^(3) + (((2 * a) * b) * c) - (a * c^(2)) - (b * c^(2))))})
k = Line(T, x10015)
radical = TriangleCurve(A, B, C, 0 = ((B * C) * a^(2)) + ((A * C) * b^(2)) + ((A * B) * c^(2)) - ((A + B + C) * ((-((((A * (a - b - c)) * ((a^(3) * b) - (a^(2) * b^(2)) - (a * b^(3)) + b^(4) + (a^(3) * c) + ((a^(2) * b) * c) - ((a * b^(2)) * c) - (b^(3) * c) - (a^(2) * c^(2)) - ((a * b) * c^(2)) - (a * c^(3)) - (b * c^(3)) + c^(4) + (((a + b - c) * (a - b + c)) * S)))) / (((a + b + c) * (a^(2) - ((2 * a) * b) + b^(2) - ((2 * a) * c) - ((2 * b) * c) + c^(2)))))) - (((B * ((-a) + b - c)) * (a^(4) - (a^(3) * b) - (a^(2) * b^(2)) + (a * b^(3)) - (a^(3) * c) - ((a^(2) * b) * c) + ((a * b^(2)) * c) + (b^(3) * c) - ((a * b) * c^(2)) - (b^(2) * c^(2)) - (a * c^(3)) - (b * c^(3)) + c^(4) + (((a + b - c) * ((-a) + b + c)) * S)))) / (((a + b + c) * (a^(2) - ((2 * a) * b) + b^(2) - ((2 * a) * c) - ((2 * b) * c) + c^(2)))) - (((C * ((-a) - b + c)) * (a^(4) - (a^(3) * b) - (a * b^(3)) + b^(4) - (a^(3) * c) - ((a^(2) * b) * c) - ((a * b^(2)) * c) - (b^(3) * c) - (a^(2) * c^(2)) + ((a * b) * c^(2)) - (b^(2) * c^(2)) + (a * c^(3)) + (b * c^(3)) + (((a - b + c) * ((-a) + b + c)) * S)))) / (((a + b + c) * (a^(2) - ((2 * a) * b) + b^(2) - ((2 * a) * c) - ((2 * b) * c) + c^(2)))))))