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SSC CGL 2025 PYQ — Question 53

SSC CGL - 16 Sep 2025 - Shift 1 • Quantitative Aptitude • Q53

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Two circles with radii r1 and r2 touch each other externally. If the length of their direct common tangent is T, Which of the following is the correct relationship btweeen T, r1 and r2?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. T = 2r1r22{\sqrt{r_1r_2} }.

For two circles touching externally:

Distance between centers = r1 + r2

Length of direct common tangent (T):

T2 = (distance between centers)2 − (1 − r2)2

⇒ (r1 + r2)2 − (r1 − r2)2

⇒ r12 + 2r1r2 + r22 − (r12 − 2r1r2 + r22) = 4r1r2

So,

T = 2r1r22{\sqrt{r_1r_2} }