Question 100
Let $OAB$ be a sector of a circle with its center $O$ as in the figure below. A point $Q$ is chosen on the chord $AB$. Let $P$ be the point of intersection of the arc of the circular sector and the line $OQ$. If $AQ = 5$, $BQ = 6$, $OQ = PQ$, determine the value of the radius of this sector. Here for a line segment $XY$, its length is also denoted by $XY$.
