A vertical pole of height 10 √ 3 meters is observed from three points, A, B and C in the same horizontal line passing through the foot ' O ' of the…

A vertical pole of height $\displaystyle 10 \sqrt{3}$ meters is observed from three points, $\displaystyle \mathrm{A}, \mathrm{B}$ and C in the same horizontal line passing through the foot ' O ' of the pole. The angles of elevation of the top, ' P ', of the pole from $\displaystyle \mathrm{A}, \mathrm{B}$ and C are in A.P. If $\displaystyle \mathrm{AP}=20 \sqrt{3}$ meters, $\displaystyle \mathrm{OC}=10$ meters and $\displaystyle \mathrm{BP}=k$ meters, then $\displaystyle k^2$ is equal to \_\_\_\_.