Question : The radii of two circles are 5 cm and 3 cm. The distance between their centre is 24 cm. Then the length of the transverse common tangent is:
Option 1: $16$ cm
Option 2: $15\sqrt{2}$ cm
Option 3: $16\sqrt{2}$ cm
Option 4: $15$ cm
Correct Answer: $16\sqrt{2}$ cm
Solution : Given, $r_1$ = 5 cm and $r_2$ = 3 cm Distance between two circles, $d$ = 24 cm We know, the length of the transverse common tangent = $\sqrt{d^2-(r_1+r_2)^2}$ = $\sqrt{24^2-(5+3)^2}$ = $\sqrt{576-64}$ = $\sqrt{512}$ = $16\sqrt{2}$ cm Hence, the correct answer is $16\sqrt{2}$ cm.
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