The Line through the Incenter and Circumcenter
Let ABC be a triangle with inradius , incenter I, and circumcenter O. Let the line OI intersect the circumcircle at D and E and the incircle at F and G, with F closer to D than to E. Then .
The statement of the theorem is in Problem 160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius.