MathNet 2015-part-01 — 191 problems (EN–VI) Question 114

Given a cyclic quadrilateral $ABCD$ with $AB = AD$. Points $M$ and $N$ are marked on the sides $CD$ and $BC$, respectively, so that $DM + BN = MN$.

Prove that the circumcenter of the triangle $AMN$ belongs to the segment $AC$.