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Locus of vertices of isosceles triangles

Source: Czech and Slovak Olympiad 1975, National Round, Problem 5

July 20, 2024
geometryLocusisoscelesTrianglessquare

Problem Statement

Let a square P=P1P2P3P4\mathbf P=P_1P_2P_3P_4 be given in the plane. Determine the locus of all vertices AA of isosceles triangles ABC,AB=BCABC,AB=BC such that the vertices B,CB,C are points of the square P.\mathbf P.
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