Školjka

Let $ABC$ be an isosceles triangle with $|AC|=|BC|$, let $M$ be the midpoint of its side $\overline{AC}$, and let $Z$ be the line through $C$ perpendicular to $\overline{AB}$. The circle through the points $B$, $C$, and $M$ intersects the line $Z$ at the points $C$ and $Q$. Find the radius of the circumcircle of the triangle $ABC$ in terms of $m = |CQ|$.