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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 .


	Contributed by: Jay Warendorff After work by: Antonio Gutierrez

The statement of the theorem is in Problem 160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius.

Circumcircle (Wolfram MathWorld)

Circumradius (Wolfram MathWorld)

Incenter (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

Inradius (Wolfram MathWorld)

"The Line through the Incenter and Circumcenter" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheLineThroughTheIncenterAndCircumcenter/

Contributed by: Jay Warendorff

After work by: Antonio Gutierrez

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