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locus of intersections of perpendicular bisectors of two equal segments is line

Source: 2019 Oral Moscow Geometry Olympiad grades 8-9 p5

May 21, 2019
geometryperpendicular bisectorLocusLocus problemscollinear

Problem Statement

Given the segment PQ PQ and a circle . A chord ABAB moves around the circle, equal to PQPQ. Let TT be the intersection point of the perpendicular bisectors of the segments APAP and BQBQ. Prove that all points of TT thus obtained lie on one line.
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