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ABC is isosceles triangle - [UKRMO 2009 Grade 11]

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January 23, 2011
geometry proposedgeometry

Problem Statement

In triangle ABCABC let MM and NN be midpoints of BCBC and AC,AC, respectively. Point PP is inside ABCABC such that ∠BAP=∠PBC=∠PCA.\angle BAP = \angle PBC = \angle PCA . Prove that if ∠PNA=∠AMB,\angle PNA = \angle AMB, then ABCABC is isosceles triangle.
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