Pythagoras - Rich Task

This is a construction approach to show that the triangle ABC is of the same area as each of the unshaded "outer" triagles on the figure.

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C

A

B

2nd Triangle

C = (8.851376471028711, 5.847345984170102)
b = Line(C, a)
c = OrthogonalLine(C, a)
A = Point(c)
B = Point(b)
poly1, b_1, a_1, c_1 = Polygon(C, B, A)
poly2, d, e, f, g, D, E = Polygon(A, B, 4)
poly3, h, i, j, k, F, G = Polygon(B, C, 4)
poly4, l, m, n, p, H, I = Polygon(C, A, 4)
J = Point(c_1)
q = Segment(H, E)
r = Segment(D, G)
s = Segment(F, I)
t = Circle(J, Segment[A, H])
d_1 = Line(J, m)
e_1 = Line(J, l)
K = Intersect(t, e_1, 2)
L, M = Intersect(t, d_1)
f_1 = AngularBisector(K, J, M)
N, O = Intersect(t, f_1)
g_1 = CircumcircleArc(M, O, K)
P = Point(g_1)
h_1 = Segment(P, J)
k_1 = Circle(J, Segment[A, E])
p_1 = Circle(P, Segment[H, E])
Q = Intersect(k_1, p_1, 2)
i_1 = Segment(J, Q)
j_1 = Segment(Q, P)
l_1 = Line(Q, i)
q_1 = Circle(Q, Segment[J, P])
R = Intersect(q_1, l_1, 1)
m_1 = Segment(Q, R)
S = Point(m_1)
poly5, p_2, j_2, s_1 = Polygon(J, S, P)
n_1 = Segment(P, A)
r_1 = Segment(J, C)
t_1 = Segment(S, B)
u = false
o = true
text4: C + ""
T = Point(b_1)
a_2 = OrthogonalLine(T, b_1)
c_2 = Circle(T, Segment[B, G])
b_2 = OrthogonalLine(T, a_2)
U, V = Intersect(c_2, b_2)
W, Z = Intersect(c_2, a_2)
d_2 = AngularBisector(W, T, U)
A_1, B_1 = Intersect(c_2, d_2)
e_2 = CircumcircleArc(W, B_1, U)
C_1 = Point(e_2)
f_2 = Segment(T, C_1)
g_2 = Circle(C_1, Segment[G, D])
h_2 = Circle(T, Segment[B, D])
D_1 = Intersect(g_2, h_2, 2)
i_2 = Segment(C_1, D_1)
k_2 = Segment(D_1, T)
l_2 = Segment(D_1, H)
m_2 = Segment(T, C)
n_2 = Segment(C_1, B)
q_2 = Line(D_1, j)
r_2 = Circle(D_1, Segment[F, G])
E_1 = Intersect(r_2, q_2, 2)
s_2 = Segment(D_1, E_1)
F_1 = Point(s_2)
t_2 = Segment(T, F_1)
a_3 = Segment(F_1, C_1)
poly6, c_3, t_3, f_3 = Polygon(T, F_1, C_1)
b_3 = Segment(F_1, J)
v = false
d_3 = Segment(F_1, A)