Question 2
Let $O$ be the centre of a regular polygon with 18 sides and vertices $A_{1}, \ldots, A_{18}$. Let $B$ be the point of $[OA_{1}]$ such that $\widehat{BA_{2}O}=20^{\circ}$ and $C$ the point of $[OA_{2}]$ such that $\widehat{CA_{1}O}=10^{\circ}$. Prove that $B, C, A_{2}, A_{3}$ are concyclic.