Problem #PRU-56573

Problems Geometry Plane geometry Circles Connection between the arc length, the angle, and the chord

Problem

From the point \(M\), moving along a circle the perpendiculars \(MP\) and \(MQ\) are dropped onto the diameters \(AB\) and \(CD\). Prove that the length of the segment \(PQ\) does not depend on the position of the point \(M.\)