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A Concurrency from Midpoints of Arcs of the Circumcircle


	Let ABC be a triangle. Let A', B', and C' be the midpoints of the arcs BC, CA, and AB of the circumcircle of ABC, respectively. Let A'B' meet BC and AC at S and T, B'C' meet AC and AB at F and P, and C'A' meet AB and BC at Q and R. Then PS, QT, and FR are concurrent.


	Contributed by: Jay Warendorff

See Harder Problems 1, Collinearity and Concurrence by Po-Shen Loh.

Circumcircle (Wolfram MathWorld)

Concurrent (Wolfram MathWorld)

"A Concurrency from Midpoints of Arcs of the Circumcircle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AConcurrencyFromMidpointsOfArcsOfTheCircumcircle/

Contributed by: Jay Warendorff

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