Question : In the following figure, two circles touch each other externally. The radius of the first circle with centre P is 25 cm. The radius of the second circle with centre Q is 4 cm. Find the length of their direct common tangent, AB. The figure is not to scale and is only for representational purposes.
Option 1: 21 cm
Option 2: 18 cm
Option 3: 20 cm
Option 4: 22 cm
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Correct Answer: 20 cm
Solution :
Here, $r_{1} = 25, r_{2} = 4$
Length of a common tangent = $\sqrt{(r_{1}+r_{2})^{2} - (r_{1}-r_{2})^{2}}$
= $\sqrt{29^{2} - 21^{2}}$
= $\sqrt{841-441}$
= $\sqrt{400}$
= $20$ cm
Hence, the correct answer is 20 cm.
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