S_{ABC}=\frac{r·(a+b+c)}{2}

A = (6.38, 4.52)
B = (-1.82, -4.58)
C = (14.82, -4.56)
t1, c, a, b = Polygon(A, B, C)
f = AngularBisector(A, C, B)
g = AngularBisector(C, B, A)
h = AngularBisector(B, A, C)
O = Intersect(h, g)
i = OrthogonalLine(O, c)
D = Intersect(i, c)
r = Segment(D, O)
d = Circle(O, D)
α = Angle(O, D, A)
tekst1: "S_{ABC}=" + (LaTeX[t1]) + ""