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