Question : Two circles of radius 10 cm and 5 cm touch each other externally at point A. PQ is the direct common tangent of those two circles of centres O1 and O2, respectively. The length of PQ is equal to:
Option 1: $10\sqrt{2}$ cm
Option 2: $8\sqrt{2}$ cm
Option 3: $9\sqrt{2}$ cm
Option 4: $6\sqrt{2}$ cm
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Correct Answer: $10\sqrt{2}$ cm
Solution : Given: Here, the radius of the first circle ($r_1$) = 10 cm And the radius of the second circle ($r_2$) = 5 cm PQ is the direct common tangent of those two circles of centres O 1 and O 2 , respectively. We know, The length of the direct common tangent = $2\sqrt{r_1×r_2}$ $\therefore$ PQ = $2\sqrt{10×5}=10\sqrt{2}$ cm Hence, the correct answer is $10\sqrt{2}$ cm.
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