Aire ADK = Aire AOI

Démarrer

Et de même :
Aire CMLG = Aire CONH

Conséquence dans le cas où (AB) ⊥ (BC) :
Le triangle ABC rectangle en B
est caractérisé par l'égalité
AC² = AB² + BC² 

donc
Aire ADJK = Aire AONI

AC² = AB² + BC²

AB²

BC²

k'' = 3
k''' = 0 (slider from 0 to 6, step 0.1)
A = (-38.605190096371636, -13.362399318478468)
B = (-33.56212140198857, 6.967471355753279)
C = (-5.037264099384332, -8.004138830696458)
poly1, c, a, b = Polygon(A, B, C)
ABC = If(Angle[A, B, C] < 180.0°, 1.0, -1.0)
E = Rotate(A, -(ABC) * 90.0°, B)
D = Rotate(B, ABC * 90.0°, A)
d = Segment(B, E)
e = Segment(D, E)
f = Segment(D, A)
BAC = If(Angle[B, A, C] < 180.0°, 1.0, -1.0)
I = Rotate(C, BAC * 90.0°, A)
H = Rotate(A, -(BAC) * 90.0°, C)
g = Segment(A, I)
h = Segment(I, H)
i = Segment(H, C)
ACB = If(Angle[A, C, B] < 180.0°, 1.0, -1.0)
G = Rotate(B, ACB * 90.0°, C)
F = Rotate(C, -(ACB) * 90.0°, B)
j = Segment(B, F)
m = OrthogonalLine(C, Line[D, E])
n = OrthogonalLine(A, Line[F, G])
p = OrthogonalLine(B, Line[I, H])
J = Intersect(m, Line[D, E])
K = Intersect(m, Line[A, B])
L = Intersect(n, Line[F, G])
M = Intersect(n, Line[B, C])
N = Intersect(p, Line[H, I])
O = Intersect(p, Line[A, C])
poly2, e_1, b_1, k_3, j_1 = Polygon(E, B, K, J)
q = Segment(B, O)
r = Segment(A, M)
s = Segment(C, K)
poly3, b_2, f_1, l_1, m_1 = Polygon(B, F, L, M)
poly4, o, c_1, h_1, n_1 = Polygon(O, C, H, N)
poly5, m_2, l_2, g_1, c_2 = Polygon(M, L, G, C)
poly6, j_2, k_4, a_1, d_1 = Polygon(J, K, A, D)
poly7, a_2, o_1, n_2, i_1 = Polygon(A, O, N, I)
k' = Min(k'', k''')
poly10, k_1, d_3, a_5 = Polygon(D, A, K)
P: k' * C + (1.0 - k') * K
poly8, p_1, d_2, a_3 = Polygon(D, A, P)
D' = Rotate(D, (k' - 1.0) * BAC * 90.0°, A)
A' = Rotate(A, (k' - 1.0) * BAC * 90.0°, A)
C' = Rotate(C, (k' - 1.0) * BAC * 90.0°, A)
poly9, c', d', a' = Polygon(D', A', C')
Q: (k' - 2.0) * O + (1.0 - (k' - 2.0)) * B
poly11, i_2, a_4, q_1 = Polygon(A, Q, I)
k = false
poly12, j_3, d_4, k_2 = Polygon(D, K, J)
poly13, l, t, r_1 = Polygon(O, N, I)
poly14, m_3, l_3, g_2, c_3 = Polygon(M, L, G, C)
poly15, s_1, t_1, e_2, f_2 = Polygon(O, C, H, N)
u = If(Angle[A, B, C] ≥ 89.9° ∧ Angle[A, B, C] ≤ 90.1°, 1.0, 0.0)
R = Intersect(Segment[A, H], Segment[C, I])
S = Intersect(Segment[B, D], Segment[A, E])
T = Intersect(Segment[B, G], Segment[C, F])