A: (0.75, 1.5)
B: (-1.25, -0.5)
C: (2, 0)
a = Segment(B, C)
b = Segment(C, A)
c = Segment(A, B)
S: (16 * Area[A, B, C]^(2))
F: (4 * Area[A, B, C] / sqrt(3))
Q: (((3 * (b^(2) + c^(2) - a^(2))) * (c^(2) + a^(2) - b^(2))) * (a^(2) + b^(2) - c^(2)))
fA(x) = (((S * F) - Q) * x^(3)) + ((Q + (((5 * S) + ((18 * a^(2)) * (a^(2) - b^(2) - c^(2)))) * F)) * x^(2)) + ((((4 * a^(2)) * S) - ((2 * (S + ((6 * a^(2)) * (a^(2) - b^(2) - c^(2))))) * F)) * x) - ((2 * a^(2)) * S)
a_0, a_1, a_2 = Root(fA)
fB(x) = (((S * F) - Q) * x^(3)) + ((Q + (((5 * S) + ((18 * b^(2)) * (b^(2) - c^(2) - a^(2)))) * F)) * x^(2)) + ((((4 * b^(2)) * S) - ((2 * (S + ((6 * b^(2)) * (b^(2) - c^(2) - a^(2))))) * F)) * x) - ((2 * b^(2)) * S)
b_0, b_1, b_2 = Root(fB)
fC(x) = (((S * F) - Q) * x^(3)) + ((Q + (((5 * S) + ((18 * c^(2)) * (c^(2) - a^(2) - b^(2)))) * F)) * x^(2)) + ((((4 * c^(2)) * S) - ((2 * (S + ((6 * c^(2)) * (c^(2) - a^(2) - b^(2))))) * F)) * x) - ((2 * c^(2)) * S)
c_0, c_1, c_2 = Root(fC)
w_A = If(a > b ∧ a > c, 1 - x(b_0) - x(c_0), x(a_0))
w_B = If(b > c ∧ b > a, 1 - x(c_0) - x(a_0), x(b_0))
w_C = If(c > a ∧ c > b, 1 - x(a_0) - x(b_0), x(c_0))
X = Barycenter({A, B, C}, {w_A, w_B, w_C})
A' = Intersect(Line[A, X], a)
d = Segment(A, A')
B' = Intersect(Line[B, X], b)
e = Segment(B, B')
C' = Intersect(Line[C, X], c)
f = Segment(C, C')
t1, c', a', b' = Polygon(A', B', C')
text1: "a'=" + a' + "
b'=" + b' + "
c'=" + c' + ""