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Prove reflections of a point over sides of a parallelogram are concyclic

Source: 2019 Philippine IMO TST3 Problem 4

May 4, 2022
geometryreflectionConcyclicparallelogram

Problem Statement

Let PP be a point in parallelogram ABCDABCD such that PA⋅PC+PB⋅PD=AB⋅BC.PA \cdot PC + PB \cdot PD = AB \cdot BC. Prove that the reflections of PP over lines ABAB, BCBC, CDCD, and DADA are concyclic.
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