# The Line through the Incenter and Circumcenter

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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 (March 2011)

After work by: Antonio Gutierrez

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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

## Permanent Citation

"The Line through the Incenter and Circumcenter"

http://demonstrations.wolfram.com/TheLineThroughTheIncenterAndCircumcenter/

Wolfram Demonstrations Project

Published: March 7 2011