Question 27
Circle $C_1$ is internally tangent to circle $C_2$ at point $A$. Let $O$ be the center of circle $C_2$. A tangent line to circle $C_1$ at point $P$ on $C_1$ goes through point $O$. Let $Q$ be the point of intersection of half-line $OP$ and circle $C_2$, and let $R$ be the point of intersection of the line tangent to circle $C_1$ at point $A$ and the line $OP$. Suppose that the radius of circle $C_2$ is $9$ and that $PQ = QR$ is satisfied. Here we denote the length of the line segment $XY$ also by $XY$. Determine the value of $OP$.
