Let $ABC$ be an isosceles triangle with $BC = a$ and $AB = AC = b$. Segment $AC$ is the base of an isosceles triangle $ADC$ with $AD = DC = a$ such that points $D$ and $B$ share the opposite sides of AC. Let $CM$ and $CN$ be the bisectors in triangles $ABC$ and $ADC$ respectively. Determine the circumradius of triangle $CMN$. (M.Rozhkova)