MathematicsHard38×since 2004Q3933A horizontal park is in the shape of a triangle OAB\mathrm{OAB}OAB with AB=16\mathrm{AB}=16AB=16. A vertical lamp post OP\mathrm{OP}OP is erected at the point O\mathrm{O}O such that ∠PAO=∠PBO=15∘\angle \mathrm{PAO}=\angle \mathrm{PBO}=15^{\circ}∠PAO=∠PBO=15∘ and ∠PCO=45∘\angle \mathrm{PCO}=45^{\circ}∠PCO=45∘, where C\mathrm{C}C is the midpoint of AB\mathrm{AB}AB. Then (OP)2(\mathrm{OP})^{2}(OP)2 is equal to :A323(3−1)\frac{32}{\sqrt{3}}(\sqrt{3}-1)332(3−1)B323(2−3)\frac{32}{\sqrt{3}}(2-\sqrt{3})332(2−3)C163(3−1)\frac{16}{\sqrt{3}}(\sqrt{3}-1)316(3−1)D163(2−3)\frac{16}{\sqrt{3}}(2-\sqrt{3})316(2−3)Check answerSkip