# A Parallelogram Defined by the Centers of Four Incircles

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Let ABC be a triangle. Let the line DEF be parallel to AC with D on AB and E on BC. Let the line FGH be parallel to AB with H on AC and G on BC. Let O, , , and be the incircles of the triangles ABC, DBE, FEG, and CGH, respectively. Then O is a parallelogram.

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 96. Similar Triangles, Incenters, Parallelogram.

## Permanent Citation

"A Parallelogram Defined by the Centers of Four Incircles"

http://demonstrations.wolfram.com/AParallelogramDefinedByTheCentersOfFourIncircles/

Wolfram Demonstrations Project

Published: March 7 2011