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Isosceles or non-degenerate triangles

Source: Brazilian Math Olympiad - University Level - Galois-Noether 2018 #6

November 24, 2019
geometrycollege contestsBrazilian Math Olympiad

Problem Statement

Given an equilateral triangle ABCABC in the plane, how many points PP in the plane are such that the three triangles APB,BPCAP B, BP C and CPACP A are isosceles and not degenerate?
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