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concyclic wanted, angle bisectors related

Source: 2014 Saudi Arabia GMO TST day I p4

July 31, 2020
geometryangle bisectorConcyclic

Problem Statement

Let ABCABC be a triangle, DD the midpoint of side BCBC and EE the intersection point of the bisector of angle ∠BAC\angle BAC with side BCBC. The perpendicular bisector of AEAE intersects the bisectors of angles ∠CBA\angle CBA and ∠CDA\angle CDA at MM and NN, respectively. The bisectors of angles ∠CBA\angle CBA and ∠CDA\angle CDA intersect at PP . Prove that points A,M,N,PA, M, N, P are concyclic.
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