Given the segment $ PQ$ and a circle . A chord $AB$ moves around the circle, equal to $PQ$. Let $T$ be the intersection point of the perpendicular bisectors of the segments $AP$ and $BQ$. Prove that all points of $T$ thus obtained lie on one line.
Problem
Source: 2019 Oral Moscow Geometry Olympiad grades 8-9 p5
Tags: geometry, perpendicular bisector, Locus, Locus problems, collinear