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What is the length (in cm) of the transverse common tangent between two circles with radii 6 cm and 4 cm, given that the distance between their centres is 14 cm?
For two circles, the length of the transverse common tangent is
$$\Rightarrow$$ $$L=\sqrt{d^2-(r_1+r_2)^2}$$
Given: $$r_1=6,\qquad r_2=4,\qquad d=14$$
$$\Rightarrow$$ $$L=\sqrt{14^2-(6+4)^2}$$
$$\Rightarrow$$ $$\sqrt{196-100}$$
$$\Rightarrow$$ $$\sqrt{96}=4\sqrt{6}$$
Hence, the length of the transverse common tangent is $$4\sqrt{6}\text{ cm}$$
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