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RU-ALLRUSSIAN 1962 Problem 10

    AB=BC\mathrm{AB} = \mathrm{BC} and M is the midpoint of AC. H is chosen on BC so that MH is perpendicular to BC. P is the midpoint of MH. Prove that AH is perpendicular to BP.

    Dataset text NuminaMath olympiads. Quoted with source.

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