Two circles of radii 8 cm and 3 cm lie outside each other, and the distance between their centres is 13 cm. What is the length of a transverse common tangent, that is, a common tangent that crosses the segment joining the centres?

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Accepted Answer

4√3 cm. A transverse common tangent has length √(d² − (r₁ + r₂)²) = √(169 − 121) = √48 = 4√3 cm. Using the difference of the radii instead of the sum gives √(169 − 25) = 12 cm, which is the length of the direct (external) common tangent, not the transverse one.

Two circles of radii 8 cm and 3 cm lie outside each other, and the distance between their centres is 13 cm. What is the length of a transverse common tangent, that is, a common tangent that crosses the segment joining the centres?

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