10. Points $A, B, C$ lie on a circle centered at $O$ with radius 7 . The perpendicular bisector of $A B$ meets the segment $B C$ at $P$ and the extension of $A C$ at $Q$. Determine the value of $O P \cdot O Q$.
10. Ans: 49

Let $R$ be the foot of the perpendicular from $O$ to $B C$. Since $\angle B A C=\angle C O R$, we have $\angle A Q O=\angle O C P$. Thus $\triangle C O P$ is similar to $\triangle Q O C$. Therefore $O C / O Q=O P / O C$ so that $O P \cdot O Q=O C^{2}=7^{2}=49$.