Question : Two circles with radii $22 \ \text{cm}$ and $16\ \text{cm}$ touch each other externally. The length of the direct common tangent is:
Option 1: $4 \sqrt{22}\ \text{cm}$
Option 2: $8 \sqrt{11} \ \text{cm}$
Option 3: $4 \sqrt{11} \ \text{cm}$
Option 4: $8 \sqrt{22} \ \text{cm}$
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Correct Answer: $8 \sqrt{22} \ \text{cm}$
Solution :
Given: $R = 22 \ \text{cm}$ and $r = 16\ \text{cm}$
Substitute the values of $r$ and $R$ in the formula $2\sqrt{R\times r}$ to get the length of the common tangent AB.
AB = $2\sqrt{R\times r} = 2\sqrt{22\times 16}=8\sqrt{22}\ \text{cm}$
Hence, the correct answer is $8\sqrt{22}\ \text{cm}$.
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