A = (0.12, 2.48)
B = (-1.24, 2.28)
C = (-0.5227614589413379, 4.3937350561591115)
BC = Distance(B, C)
CA = Distance(C, A)
eq2: ((x(B) - (x(A) + x(B) + x(C) + x) / 4)^(2) + (y(B) - (y(A) + y(B) + y(C) + y) / 4)^(2))^(2) = (1 / 16 * ((CA^(2) + (x(C) - x)^(2) + (y(C) - y)^(2) + (x(A) - x)^(2) + (y(A) - y)^(2))^(2) - (12 * ((x(C) * y(A)) - (x(A) * y(C)) + (x(A) * y) - (x * y(A)) + (x * y(C)) - (x(C) * y))^(2))))
AB = Distance(A, B)
eq3: ((x(C) - (x(A) + x(B) + x(C) + x) / 4)^(2) + (y(C) - (y(A) + y(B) + y(C) + y) / 4)^(2))^(2) = (1 / 16 * ((AB^(2) + (x(A) - x)^(2) + (y(A) - y)^(2) + (x(B) - x)^(2) + (y(B) - y)^(2))^(2) - (12 * ((x(A) * y(B)) - (x(B) * y(A)) + (x(B) * y) - (x * y(B)) + (x * y(A)) - (x(A) * y))^(2))))
AC = Distance(A, C)
eq4: ((x - (x(A) + x(B) + x(C) + x) / 4)^(2) + (y - (y(A) + y(B) + y(C) + y) / 4)^(2))^(2) = (1 / 16 * ((AB^(2) + BC^(2) + CA^(2))^(2) - (48 * Area[A, B, C]^(2))))
D, E, F, H = Intersect(eq3, eq4)
G: (A + B + C + D) / 4
AG = Distance(A, G)
CD = Distance(C, D)
DB = Distance(D, B)
a: AG - (1 / 2 * ((BC^(2) + CD^(2) + DB^(2))^(2) - (48 * Area[B, C, D]^(2)))^(1 / 4))
BG = Distance(B, G)
DA = Distance(D, A)
b: BG - (1 / 2 * ((AC^(2) + CD^(2) + DA^(2))^(2) - (48 * Area[A, C, D]^(2)))^(1 / 4))
CG = Distance(C, G)
BD = Distance(B, D)
c: CG - (1 / 2 * ((AB^(2) + BD^(2) + DA^(2))^(2) - (48 * Area[A, B, D]^(2)))^(1 / 4))
DG = Distance(D, G)
d: DG - (1 / 2 * ((AB^(2) + BC^(2) + CA^(2))^(2) - (48 * Area[A, B, C]^(2)))^(1 / 4))
eq1: ((x(A) - (x(A) + x(B) + x(C) + x) / 4)^(2) + (y(A) - (y(A) + y(B) + y(C) + y) / 4)^(2))^(2) = (1 / 16 * ((BC^(2) + (x(C) - x)^(2) + (y(C) - y)^(2) + (x(B) - x)^(2) + (y(B) - y)^(2))^(2) - (12 * ((x(B) * y(C)) - (x(C) * y(B)) + (x(C) * y) - (x * y(C)) + (x * y(B)) - (x(B) * y))^(2))))