Question 133

The distance between centers of two circles of radii 3 cm and 8 cm is 13 cm. If the points of contact of a direct common tangent to the circles are P and Q, the length of the line segment PQ is:

Solution

Two circles having radii $$r_1$$ and $$r_2$$ and distance between them $$d$$

Length of direct common tangent PQ = $$\sqrt{d^2-(r_2-r_1)^2}$$

= $$\sqrt{(13)^2-(8-3)^2}$$

= $$\sqrt{169-25}=\sqrt{144}=12$$ cm

=> Ans - (C)

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