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The locus of midpoints of unit segments in a square

Source: Italy MO 2024 P2

May 15, 2024
geometrygeometry proposedLocus

Problem Statement

We are given a unit square in the plane. A point MM in the plane is called median if there exists points PP and QQ on the boundary of the square such that PQPQ has length one and MM is the midpoint of PQPQ. Determine the geometric locus of all median points.
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