Infinite tangents

A circle with centre point O and radius R is drawn. Point \(P_1\) is lying out of the circle such that \(\overline{OP_1}=3\). \(\overline{P_1B}\) is a tangent to the circle. Point \(P_2, P_3, ... \) till \((\infty)\) are taken on \(\overline{P_1B}\) such that \(\forall n\in\mathbb{N} P_{n+1}\) is mid point of \(\overline{P_nB}\) \(\forall n\in\mathbb{N}\overline{P_nA_n}\) is a tangent to the circle different from \(\overline{P_nB}\). If: \[\sum_{n=1}^{\infty}ar(BP_nA_nO)=2\sqrt{14}\] Find the sum of all possible values of \(R^2\) **Note:** - \(ar(X)\) is the area of plane figure \(X\)