JEE Math Practice Question

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

1. A.$$\frac{32}{\sqrt{3}}(\sqrt{3}-1)$$
2. B.$$\frac{32}{\sqrt{3}}(2-\sqrt{3})$$
3. C.$$\frac{16}{\sqrt{3}}(\sqrt{3}-1)$$
4. D.$$\frac{16}{\sqrt{3}}(2-\sqrt{3})$$