Question : Two circles of radii 9 cm and 4 cm, respectively, touch each other externally at point $A. PQ$ is the direct common tangent of those two circles of centres $O_1$ and $O_2$, respectively. The length of $PQ$ is equal to:
Option 1: 13 cm
Option 2: 11 cm
Option 3: 10 cm
Option 4: 12 cm
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Correct Answer: 12 cm
Solution :
Given: $R_1$ = 9 cm
$R_2$ = 4 cm
Thus, direct common tangent, PQ = $2\sqrt{R_1R_2}$
= $2×\sqrt{9×4}$
= $2×3×2$
= $12$ cm
Hence, the correct answer is 12 cm.
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