MathNet 2017-part-02 — 176 problems (EN–VI) Question 58

Let $ABCD$ be a convex quadrilateral such that $\angle ABC = \angle ACD$ and $\angle ACB = \angle ADC$. Suppose that the circumcenter $O$ of triangle $BCD$ is different from $A$. Prove that the angle $OAC$ is right. (Patrik Bak)