KVPY SX SB Exam 2015 Question Paper

Circles C${}_1$ and C${}_2$, of radii r and R respectively, touch each other as shown in the figure. The line l, which is parallel to the line joining the centres of C${}_1$ and C${}_2$, is tangent to C${}_1$ at P and intersects C${}_2$ at A, B. If ${\mathit{R}}^2=2{\mathit{r}}^2$, then $\angle \mathit{A}\mathit{O}\mathit{B}$ equals -