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PQ _|_BC wanted, 45^o given, isosceles (2016 From Tasks to Tasks, p13 Ukr)

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May 3, 2021
geometryperpendicularisosceles

Problem Statement

Let ABCABC be an isosceles acute triangle (AB=BCAB = BC). On the side BCBC we mark a point PP, such that ∠PAC=45o\angle PAC = 45^o, and QQ is the point of intersection of the perpendicular bisector of the segment APAP with the side ABAB. Prove that PQ⊥BCPQ \perp BC.
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