IT-CESENATICO 2002 Problem 3

Let $A$ and $B$ are two points on a plane, and let $M$ be the midpoint of $AB$ . Let $r$ be a line and let $R$ and $S$ be the projections of $A$ and $B$ onto $r$ . Assuming that $A$ , $M$ , and $R$ are not collinear, prove that the circumcircle of triangle $AMR$ has the same radius as the circumcircle of $BSM$ .