MathNet 2016-part-06 — 184 problems (EN–VI) Question 94

Let $AXYZB$ be a convex pentagon inscribed in a semicircle with diameter $AB$, and let $K$ be the foot of the altitude from $Y$ to $AB$. Let $O$ denote the midpoint of $AB$ and $L$ the intersection of $XZ$ with $YO$. Select a point $M$ on line $KL$ with $MA = MB$, and finally, let $I$ be the reflection of $O$ across $XZ$.
Prove that if quadrilateral $XKOZ$ is cyclic then so is quadrilateral $YOMI$.