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parallelogram wanted, similar triangles on each side of a triangle

Source: 2011 Portugal p2

October 10, 2020
geometryparallelogramsimilar triangles

Problem Statement

The point PP, inside the triangle [ABC][ABC], lies on the perpendicular bisector of [AB][AB]. QQ and RR points, exterior to the triangle, they are such that [BPA],[BQC] [BPA], [BQC] and [CRA][CRA] are similar triangles. Shows that [PQCR][PQCR] is a parallelogram. https://cdn.artofproblemsolving.com/attachments/f/5/6e036b127f8a013794b8246cbb1544e7280d4a.png
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