Multiple choice

If distance between centres of two circles is $a$ and radii are $r_{1}$and $r_{2}$ , then length of common tangent is

  1. $r_{1}+r_{2}$
  2. $a^{2}$
  3. $\sqrt{a^{2}-(r_{1}+r_{2})^{2}}$

  4. none of these
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C Correct answer
Explanation

The length of the transverse (or indirect) common tangent between two circles with radii r1 and r2 and distance between centers a is given by the formula sqrt(a^2 - (r1 + r2)^2). This is derived using the Pythagorean theorem on the right triangle formed by the centers and the parallel shift of the tangent.

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