CONO-SUR 1997 Problem 2

Let $C$ be a circunference, $O$ is your circumcenter, $AB$ is your diameter and $R$ is any point in $C$ ( $R$ is different of $A$ and $B$ ) Let $P$ be the foot of perpendicular by $O$ to $AR$ , in the line $OP$ we match a point $Q$ , where $QP$ is $\frac{OP}{2}$ and the point $Q$ isn't in the segment $OP$ . In $Q$ , we will do a parallel line to $AB$ that cut the line $AR$ in $T$ . Denote $H$ the point of intersections of the line $AQ$ and $OT$ . Show that $H$ , $B$ and $R$ are collinears.