Circle \(C_1\) and \(C_2\) of radii \(r\) and \(R\) respectively, touch each other as shown in f....

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Circle \(C_1\) and \(C_2\) of radii \(r\) and \(R\) respectively, touch each other as shown in figure. The line \(l_1\) 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 \(R^2=2 r^2\), then \(\angle A O B\) equals
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