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The radii of two circles are 5 cm and 10 cm, and the distance between their centres is 17 cm. Find the length of the transverse common tangent.
- 9 cm
- 8 cm
- 6 cm
- 7.5 cm
Correct answer: 8 cm
Solution
For two circles, the length of the transverse common tangent is \(\sqrt{d^2-(r_1+r_2)^2}\). Substituting \(d=17\), \(r_1=5\), and \(r_2=10\), we get \(\sqrt{17^2-15^2} = \sqrt{289-225} = \sqrt{64} = 8\). Hence, the answer is 8 cm.
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