Exams › SSC CGL (Prelims) › General

Two circles with radii r1 and r2 touch each other internally. If the length of their common tangent is T, which relationship correctly links T, r1 and r2?

1. T = 2(r1 - r2)
2. T = sqrt(r1^2 - r2^2)
3. T = r1 - r2
4. T = 2*sqrt(r1*r2)

Correct answer: T = 2*sqrt(r1*r2)

Solution

For two circles touching internally, the length of the common (transverse-style) tangent works out to T = 2*sqrt(r1*r2). This is the standard derived relation for internally tangent circles.

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