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This section has Four Questions. Each question is provided with 4 alternative answers. Exactly one of them is the correct answer. Indicate the correct answer by A, B, C, D.
Two circles having different radii are touching each other. A common tangent $$\overleftrightarrow{PQ}$$ is touching one circle at $$P$$ and the other at $$Q$$. If $$PQ = 12$$ then the product of their radii is equal to
For circles of radii $$r_1$$, $$r_2$$ touching externally, the distance between centres is $$r_1 + r_2$$. The length of the direct common tangent is $$PQ = \sqrt{(r_1 + r_2)^2 - (r_1 - r_2)^2} = 2\sqrt{r_1 r_2}$$. So $$144 = 4r_1 r_2$$ and $$r_1 r_2 = 36$$.
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