The Product of the Circumradius and an Exradius

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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 .

Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA



The statement of the theorem is in Problem 156. Triangle, Circumradius, Exradius, Chord, Secant line.

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