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<ABM=<MBP wanted, AB //PC , PM_|_BM , median (2021 Kyiv City MO 8.4)

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February 16, 2021
geometryequal anglesangles

Problem Statement

Let BMBM be the median of the triangle ABCABC, in which AB>BCAB> BC. Point PP is chosen so that AB∥PCAB \parallel PC and PM⊥BMPM \perp BM. Prove that ∠ABM=∠MBP\angle ABM = \angle MBP.
(Mikhail Standenko)
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