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 .