Multiple choice

If the distance between the centres of two circles of radii 3, 4 units is 25, then the length of their transverse common tangent is

  1. $24$
  2. $12$
  3. $2$6
  4. $13$
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A Correct answer
Explanation

Length of transverse common tangent = sqrt(d^2 - (r1 + r2)^2), where d is the distance between centers. d = 25, r1 = 3, r2 = 4. Length = sqrt(25^2 - (3+4)^2) = sqrt(625 - 49) = sqrt(576) = 24.

AI explanation

The length of the transverse common tangent between two circles with radii r1 and r2 and distance d between their centers is given by the square root of (d squared minus (r1 plus r2) squared). Substituting the given values, we find the square root of (25 squared minus (3 plus 4) squared), which is the square root of (625 minus 49). The square root of 576 is 24.

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