A horizontal park is in the shape of a triangle O A B with A B=16. A vertical lamp post OP is erected at the point O such that ∠ PAO =∠ PBO =15^° and…

A horizontal park is in the shape of a triangle $\displaystyle O A B$ with $\displaystyle A B=16$. A vertical lamp post OP is erected at the point O such that $\displaystyle \angle \mathrm{PAO}=\angle \mathrm{PBO}=15^{\circ}$ and $\displaystyle \angle \mathrm{PCO}=45^{\circ}$, where $\displaystyle C$ is the midpoint of $\displaystyle A B$. Then $\displaystyle (O P)^2$ is equal to