Exams › SSC CGL (Prelims) › General

Two circles with radii \(r_1\) and \(r_2\) touch each other internally. If the length of their common tangent is \(T\), which of the following is the correct relationship between \(T\), \(r_1\), and \(r_2\)?

1. T = 2(r₁ - r₂)
2. T = √(r₁² - r₂²)
3. T = r₁ - r₂
4. T = 2√(r₁r₂)

Correct answer: T = 2√(r₁r₂)

Solution

For two circles, the length of the common internal tangent depends on the distance between centers and the radii. In the internally touching case, the standard relation simplifies to \(T=2\sqrt{r_1r_2}\).

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