Question 1
Let $ABC$ be a triangle inscribed in a circle $(O)$. A diameter $KL$ passes through the midpoint $M$ of $AB$, with $L$ and $C$ on opposite sides of $AB$. A circle through $M$ and $K$ intersects $LC$ at $P$ and $Q$, where $P$ lies between $Q$ and $C$. The line $KQ$ meets the circle $(LMQ)$ again at $R$. Prove that $ARBP$ is cyclic and that $AB$ is the $A$-symmedian of triangle $APR$.