\sqrt {R (R - 2r)}

A = (5, 2)
B = (13, 10)
C = (1, 10)
Vieleck1, c, a, b = Polygon(A, B, C)
d = LineBisector(a)
e = LineBisector(b)
f = LineBisector(c)
U = Intersect(d, f)
g, h = AngularBisector(c, b)
i, j = AngularBisector(a, c)
k, l = AngularBisector(a, b)
I = Intersect(h, l)
p = Circle(U, B)
q = Circle(I, Distance[I, a])
m = OrthogonalLine(I, a)
D = Intersect(m, a)
r_I = Segment(I, D)
r_U = Segment(U, B)
Text1: "Abstand |UI| = " + (Distance[U, I])
Text3: " = " + (sqrt(r_U * (r_U - 2.0 * r_I)))
n = Segment(I, U)