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Locus problem with bounded areas

Source: Czech and Slovak Olympiad 1974, National Round, Problem 6

July 19, 2024
geometrygeometric transformationrotationLocusareassquare

Problem Statement

Let a unit square D\mathcal D be given in the plane. For any point XX in the plane denote DX\mathcal D_X the image of D\mathcal D in rotation with respect to origin XX by +90∘.+90^\circ. Find the locus of all XX such that the area of union D∪DX\mathcal D\cup\mathcal D_X is at most 1.5.
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