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<OAC=2 <BPM wanted, AB = AC, <PBA = <PCB

Source: 2017 Baltic Way Shortlist G7 BW https://artofproblemsolving.com/community/c2659348_baltic_way_shortlist_2017_geometry

November 25, 2021
equal anglesgeometry

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB = AC. Let P be a point in the interior of ABCABC such that PB>PCPB > PC and ∠PBA=∠PCB\angle PBA = \angle PCB. Let MM be the midpoint of the side BCBC. Let OO be the circumcenter of the triangle APMAPM. Prove that ∠OAC=2∠BPM\angle OAC=2 \angle BPM .
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