Circumscribing a Triangle

Experiment with acute, right, and obtuse triangles.
What happens to the point of intersection?

First bisect each side of the triangle.
(Details are not shown.)

The bisectors will share
a common point.

A = (1.28, 4.14)
B = (-2.44, -0.52)
C = (6.28, -1.44)
poly1, c, a, b = Polygon(A, B, C)
d = LineBisector(c)
e = LineBisector(a)
f = LineBisector(b)
D = Intersect(d, f)
g = Circle(D, A)