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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