RMM 2026 Problem 5

Let $ABC$ be a triangle with $AB < AC$, let $O$ be its circumcentre and let $XYZT$ be a parallelogram inside triangle $ABC$ such that

$$\angle AXB = \angle AZC, \angle AZB = \angle AXC,$$

$$\angle AYB = \angle ATC, \angle ATB = \angle AYC.$$

Prove that the diagonals $XZ$ and $YT$ of the parallelogram intersect on the circumcircle of $BOC$.