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


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The statement of the theorem is in Problem 96. Similar Triangles, Incenters, Parallelogram.



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