Problem 160.
Triangle, Incircle, Incenter, Circumcircle, Circumcenter,
Inradius
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
 .
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