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A Concurrency of Lines through Points of Tangency with Excircles


	Let ABC be a triangle with orthocenter H. Let be the point of tangency of CA with the excircle opposite A, and similarly define , , , , and . Let , , and . Let , , and . Then AA', BB', and CC' as well as AA'', BB'', and CC'' meet at H.


	Contributed by: Jay Warendorff After work by: Paul Yiu

See the paper "Synthetic proof of Paul Yiu's excircles theorem" available on Darij Grinberg's home page.

Concurrent (Wolfram MathWorld)

Excircles (Wolfram MathWorld)

Orthocenter (Wolfram MathWorld)

"A Concurrency of Lines through Points of Tangency with Excircles" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AConcurrencyOfLinesThroughPointsOfTangencyWithExcircles/

Contributed by: Jay Warendorff

After work by: Paul Yiu

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