The Product of the Circumradius and an Exradius
Let ABC be a triangle with circumradius . Construct the excircle opposite A with excenter F and exradius . Let D and E be the intersections of the extensions of AB and AC with the excircle. Let G be the intersection of AF with the circumcircle of ABC. Then .
The statement of the theorem is in Problem 156. Triangle, Circumradius, Exradius, Chord, Secant line.