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Uniquely determined side

Source: Original RMM 2019 P4

June 21, 2020
geometryEquilateral Trianglecircumcirclecontest problem

Problem Statement

Let there be an equilateral triangle ABCABC and a point PP in its plane such that AP<BP<CP.AP<BP<CP. Suppose that the lengths of segments AP,BPAP,BP and CPCP uniquely determine the side of ABCABC. Prove that PP lies on the circumcircle of triangle ABC.ABC.
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