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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
After work by: Antonio Gutierrez

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

Circumcircle (Wolfram MathWorld)

Excircles (Wolfram MathWorld)

"The Product of the Circumradius and an Exradius" from the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheProductOfTheCircumradiusAndAnExradius/

Contributed by: Jay Warendorff

After work by: Antonio Gutierrez

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The Product of the Circumradius and an Exradius

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