Pripísané kružnice a obvod trojuholníka

\text{Osi vnútorných a vonkajších uhlov }\triangle ABC

J_i \text{ stredy pripísaných kružníc }\triangle ABC

a_1

a_1

| AT_1|=|AC |+|CT_1 |= b+a_1

a_2

a_2

| AT_2|=|AB |+|BT_2 |= c+a_2

| AT_1|+|AT_2 |= b+c+ (a_1+a_2)=O_{ABC}

| AT_1| =| AT_2| \;  ⇒ \; | AT_i| =\frac{O_{ABC}}{2}

A = (-1.9697030798979434, -0.3942632345909858)
B = (4.152195256968027, 2.0208314456439433)
C = (0.7589402055376696, 5.626164937788711)
t1, c, a, b = Polygon(A, B, C)
f = Line(A, B)
i = Line(A, C)
r = Line(B, C)
g, h = AngularBisector(i, f)
j, k = AngularBisector(r, i)
l, m = AngularBisector(f, r)
I = Intersect(g, j)
p = OrthogonalLine(I, r)
E = Intersect(r, p)
k_1 = Circle(I, E)
J_A = Intersect(g, l)
n = OrthogonalLine(J_A, r)
D = Intersect(r, n)
J_B = Intersect(h, k)
J_C = Intersect(h, j)
c_1 = Circle(J_A, D)
g_1 = OrthogonalLine(J_B, i)
h_1 = OrthogonalLine(J_C, f)
G = Intersect(f, h_1)
F = Intersect(i, g_1)
e_1 = Circle(J_B, F)
d_1 = Circle(J_C, G)
i_1 = OrthogonalLine(J_A, i)
j_1 = OrthogonalLine(J_A, f)
T_1 = Intersect(c_1, i, 1)
T_2 = Intersect(c_1, f, 2)
l_1 = Segment(J_A, T_1)
m_1 = Segment(J_A, D)
n_1 = Segment(J_A, T_2)
p_1 = Segment(C, D)
q_1 = Segment(C, T_1)
r_1 = Segment(B, D)
s_1 = Segment(B, T_2)