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Locus of vertices of equilateral triangles

Source: Czech and Slovak Olympiad 1971, National Round, Problem 5

July 9, 2024
geometryEquilateralTrianglesLocus

Problem Statement

Let ABCABC be a given triangle. Find the locus M\mathbf M of all vertices ZZ such that triangle XYZXYZ is equilateral where XX is any point of segment ABAB and Y≠XY\neq X lies on ray AC.AC.
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