# The Radii of Four Incircles

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Let ABC be a triangle. Let DEF be parallel to AC with D on AB and E on BC. Let FGH be parallel to AB with G on BC and H on AC. Let , , , and be the radii of the incircles O, , , of the triangles ABC, DBE, FEG, and CGH, respectively. Then , with the plus sign when F is outside of ABC and minus when F is inside.

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 95. Similar Triangles, Inradii, Parallel.

## Permanent Citation

"The Radii of Four Incircles"

http://demonstrations.wolfram.com/TheRadiiOfFourIncircles/

Wolfram Demonstrations Project

Published: March 7 2011