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A Concurrency from Circumcircles of Subtriangles


	Let ABC be a triangle and let the incircle intersect BC, CA, and AB at A', B', and C', respectively. Let the circumcircles of AB'C', A'BC', and A'B'C intersect the circumcircle of ABC (apart from A, B, and C) at A'', B'', and C'', respectively. Then A'A'', B'B'', and C'C'' are concurrent.


	Contributed by: Jay Warendorff

See Four Circles—a problem from the Canadian Mathematical Olympiad 2007.

Circumcircle (Wolfram MathWorld)

Concurrent (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

"A Concurrency from Circumcircles of Subtriangles " from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AConcurrencyFromCircumcirclesOfSubtriangles/

Contributed by: Jay Warendorff

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