Can we find the ratio of the areas of these two sectors?

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The figure shows two circles, centres \(O\) and \(C\), radii \(r_1\) and \(r_2\), which touch externally at \(P\). Given that \(A\hat{O}P=\dfrac{\pi}{4}\) radians, \(B\hat{C}P = \dfrac{\pi}{3}\) radians and \(AB\) is parallel to \(OPC\), show that \(\dfrac{r_1}{r_2} = \dfrac{\sqrt{6}}{2}\). Hence find the ratio of the areas of the sectors \(OAP\), \(CBP\).