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Concurrent Line Segments Related to the Incircle

Let ABC be a triangle. Let the intersection of the incircle with BC be A'. Let AA' also intersect the incircle at P. Let BP and CP intersect the incircle at M and N, respectively. Then CM, BN, and AA' are concurrent.

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See Iranian Mathematical Olympiad 2002 Third Round 3/6.

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"Concurrent Line Segments Related to the Incircle" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ConcurrentLineSegmentsRelatedToTheIncircle/
Contributed by: Jay Warendorff
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