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locus of midpoints of segments of fixed length, moving on sides of square

Source: 1962-63 Germany R4 12.5 https://artofproblemsolving.com/community/c3208025_

October 12, 2024
geometryLocusmidpointsquare

Problem Statement

Given is a square with side length aa. A distance PQPQ of length pp, where p<ap < a, moves so that its end points are always on the sides of the square. What is the geometric locus of the midpoints of the segments PQPQ?
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