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Return of the geo king

Source: Kyiv City MO 2021 Round 1, Problem 8.4

December 21, 2023
geometry

Problem Statement

Let BMBM be the median of the triangle ABCABC with AB>BCAB > BC. The point PP is chosen so that AB∥PCAB\parallel PC and PM⊥BMPM \perp BM. Prove that ∠ABM=∠MBP\angle ABM = \angle MBP.
Proposed by Mykhailo Shandenko
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