C = (6, 0)
B = (0, 0)
A: (10 + 1 / 3, sqrt(62 + 2 / 9))
t1, c, a, b = Polygon(A, B, C)
g_c(λ) = coth(((c * λ)) / (a + b + c))
w(λ) = (c * g_c(λ))
g_b(λ) = coth(((b * λ)) / (a + b + c))
v(λ) = (b * g_b(λ))
g_a(λ) = coth(((a * λ)) / (a + b + c))
Z(λ) = sqrt((((g_c(λ))^(2) - 1) * (c^(2) - ((a * g_a(λ)) - (b * g_b(λ)))^(2))))
u(λ) = (a * g_a(λ))
f(λ) = sqrt((((u(λ))^(2) - a^(2)) * (a^(2) - (v(λ) - w(λ))^(2)))) + sqrt((((v(λ))^(2) - b^(2)) * (b^(2) - (w(λ) - u(λ))^(2)))) + sqrt((((w(λ))^(2) - c^(2)) * (c^(2) - (u(λ) - v(λ))^(2)))) - sqrt((2 * ((b^(2) * c^(2)) + (c^(2) * a^(2)) + (a^(2) * b^(2)))) - a^(4) - b^(4) - c^(4))
L = Intersect(f, xAxis, (4.654744689440924, 0))
λ_P: x(L)
Y(λ) = sqrt((((g_b(λ))^(2) - 1) * (b^(2) - ((c * g_c(λ)) - (a * g_a(λ)))^(2))))
X(λ) = sqrt((((g_a(λ))^(2) - 1) * (a^(2) - ((b * g_b(λ)) - (c * g_c(λ)))^(2))))
x_P: X(λ_P)
y_P: Y(λ_P)
z_P: Z(λ_P)
X_{5626}: (((a * x_P) * A) + ((b * y_P) * B) + ((c * z_P) * C)) / ((a * x_P) + (b * y_P) + (c * z_P))
d_{AB} = Distance(X_{5626}, Segment[A, B])
d_{AC} = Distance(X_{5626}, Segment[A, C])
d_{BC} = Distance(X_{5626}, Segment[B, C])