Question 75

The distance between the centre of two circles of radius 4 cm and 2 cm is 10 cm. The length (in cm) of a transverse common tangent is:

Solution

Given, distance between centres of circles$$(d)$$ = 10 cm

Radius of first circle$$(r_1)$$ = 4 cm

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

$$\therefore\ $$The length of tranverse common tangent = $$\sqrt{d^2-\left(r_1+r_2\right)^2}=\sqrt{10^2-\left(4+2\right)^2}=\sqrt{100-36}=8\ cm$$

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