Q = (4, 5)
P = (-3, 5)
B = (0.4, 2.34)
C = (3.98, 2.32)
a_1 = Segment(P, Q)
A = (0.74, 5.26)
poly1, c, a, b = Polygon(A, B, C)
C' = Midpoint(A, B)
A' = Midpoint(B, C)
B' = Midpoint(C, A)
d = AngularBisector(B, A, C)
e = AngularBisector(A, B, C)
f = AngularBisector(B, C, A)
I = Intersect(f, d)
g = OrthogonalLine(A, d)
h = OrthogonalLine(B, e)
Jb = Intersect(g, e)
Jc = Intersect(h, f)
Ja = Intersect(h, d)
i = Line(A, B)
j = Line(A, C)
k = OrthogonalLine(C, i)
l = OrthogonalLine(B, j)
H = Intersect(k, l)
m = Line(H, A)
n = Line(B, C)
D = Intersect(m, n)
E = Intersect(l, j)
F = Intersect(k, i)
G: (A + B + C) / 3
B'' = Mirror(B', e)
A'' = Mirror(A', d)
p = Line(B, B'')
q = Line(A, A'')
L = Intersect(p, q)
J = Midpoint(A, D)
K = Midpoint(B, E)
M = Midpoint(C, F)
r = Circle(A, B, C)
O = Center(r)
s = OrthogonalLine(I, i)
N = Intersect(s, i)
t = Circle(I, N)
o = ImplicitCurve({A, B, C, A', B', C', Ja, Jb, Jc})
Pc = Intersect(i, f)
b_1 = OrthogonalLine(C, f)
Qc = Intersect(i, b_1)
Pb = Intersect(e, j)
Qb = Intersect(h, j)
Pa = Intersect(d, n)
Qa = Intersect(g, n)
R, S, T, U, V, W = Intersect(o, r)
v = ImplicitCurve({R, S, T, U, V, W, Ja, Jb, Jc, Pa, Pb, Pc, I, O})
c_1 = Conique2Tgtes(j, E, i, F, D)
F_1, F_2 = Focus(c_1)

Tool: Conique2Tgtes
Input: a, A, b, B, C
Output: k

A = Point(a)
B = Point(b)
c = Line(B, C)
M = Point(c)
K = Intersect(a, b)
d = Line(K, M)
e = Line(C, A)
L = Intersect(d, e)
f = Line(A, M)
g = Line(B, L)
D = Intersect(f, g)
G = Point(e)
h = Line(K, G)
H = Intersect(c, h)
i = Line(A, H)
j = Line(B, G)
E = Intersect(i, j)
k = Conic(A, B, C, D, E)