Problem 155.
Euler's Theorem: Distance from the Incenter to the
Circumcenter

In the figure below, ABC is a
triangle inscribed in a circle of center O (circumcenter) and
circumscribed in a circle of center I (incenter). If d is the
distance from the incenter to the circumcenter prove that:
.

Geometric Art: Hyperbolic Kaleidoscope of problem
155 using iPad Apps