you can drag the red points

A = (8, 8)
B = (7, 5)
C = (10, 5)
a = Line(B, A)
b = Line(B, C)
c = Line(C, A)
d, e = AngularBisector(a, c)
f, g = AngularBisector(a, b)
h, i = AngularBisector(b, c)
I_a = Intersect(d, g)
I_b = Intersect(h, f)
I_c = Intersect(e, i)
I = Intersect(d, i)
j = OrthogonalLine(I, b)
k = OrthogonalLine(I_a, b)
l = OrthogonalLine(I_b, c)
m = OrthogonalLine(I_c, a)
H = Intersect(j, b)
I_1 = Intersect(l, c)
J = Intersect(m, a)
K = Intersect(k, b)
p = Circle(I_c, J)
q = Circle(I_a, K)
r = Circle(I_b, I_1)
s = Circle(I, H)
L, D = Intersect(q, a)
M, G = Intersect(q, c)
N, W = Intersect(r, b)
O, F = Intersect(r, a)
P, V = Intersect(p, c)
Q, U = Intersect(p, b)
R, T = Intersect(s, c)
S, E = Intersect(s, a)
α = Angle(B, A, I)
β = Angle(I, A, R)
γ = Angle(R, C, I)
δ = Angle(I, C, H)
ε = Angle(K, B, I)
ζ = Angle(I, B, J)
η = Angle(P, A, I_c)
θ = Angle(I_c, A, J)
ι = Angle(L, B, I_a)
κ = Angle(I_a, B, K)
λ = Angle(N, C, I_b)
μ = Angle(I_b, C, R)
n = Segment(A, I_a)
t = Segment(B, I_b)
a_1 = Segment(C, I_c)
b_1 = Segment(I_c, I_b)
c_1 = Segment(I_b, I_a)
d_1 = Segment(I_a, I_c)
e_1 = Segment(B, I_1)
f_1 = Segment(K, A)
g_1 = Segment(C, J)
Nagel = Intersect(e_1, f_1)