MathDB

points moving around circles

Source: Mongolia MO 2000 Teachers P3

April 22, 2021

geometry

Problem Statement

Two points

A

and

B

move around two different circles in the plane with the same angular velocity. Suppose that there is a point

C

which is equidistant from

A

and

B

at every moment. Prove that, at some moment,

A

and

B

will coincide.