MathDB

4

Part of 2019 Philippine TST

Problems(1)

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

Source: 2019 Philippine IMO TST3 Problem 4

5/4/2022
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.
geometryreflectionConcyclicparallelogram