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Question 131
PQ is a direct common tangent of two circle of radii $$r_{1}$$Â and $$r_{2}$$Â touching each other externally at A. Then the value of PQ2 is
Solution
As we know formula for common tangent is $$PQ^2= d^2-(r_1^2-r_2^2)$$
where $$d$$ is distance between circles , PQ is common tangent $$r_1$$ and $$r_2$$ are radii of circles.
So $$PQ^2 = (r_1+r_2)^{2}-(r_1 ^2-r_2^2)^{2}$$
or $$4r_1 r_2$$
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