Question 53

The distance between the centres of two circles of radius 3 cm and 2 cm is 13 cm. The length (in cm) of a transverse common tangent is:

Solution

Radius of first circle ($$r_1$$) = 3 cm

Radius of second circle ($$r_2$$) = 2 cm

The distance between centres of two circles ($$d$$) = 13 cm

$$\therefore\ $$Length of the common tangent = $$\sqrt{d^2-\left(r_1+r_2\right)^2}$$

$$=\sqrt{13^2-\left(3+2\right)^2}$$

$$=\sqrt{169-25}$$

$$=\sqrt{144}$$

$$=$$ 12 cm

Hence, the correct answer is Option B

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