Online Geometry Problem 160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter,
Inradius.
Level: High School, Honors Geometry, College,
Mathematics Education

In the figure below, ABC is a triangle
inscribed in a circle of center O (circumcenter) and I is the incenter.
Line OI meets the circumcircle O and the incircle I at D, E, F,
and G respectively. If r is the inradius, d = DF, and e = EG, prove that
.