Triangle and intersecting lines

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It is given triangle ABC. M is the tangent point of incircle (k) and the side AB. N is the intersection point of k and CM. P is the intersection point of k and AN. Q is the intersection point of k and BN. Prove AQ, BP and CM intersects at a common point.

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If someone is interested a solution can be found at:
http://www.artofproblemsolving.com/Foru ... 8&t=370366