Multiple choice

The distance between the centres of two circles of radii 3 cm and 8 cm is 13 cm. If PQ is the direct common tangent of the circles, then its length is

  1. 11 cm

  2. 12 cm

  3. 13 cm

  4. 14 cm
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B Correct answer
Explanation

The length of the direct common tangent is sqrt(d^2 - (R - r)^2), where d is the distance between centers, and R and r are radii. Length = sqrt(13^2 - (8 - 3)^2) = sqrt(169 - 25) = sqrt(144) = 12.

AI explanation

Using the formula for the length of a direct common tangent, L = sqrt(d^2 - (r1 - r2)^2), we substitute the given values. The length is L = sqrt(13^2 - (8 - 3)^2), which simplifies to sqrt(169 - 25). This yields sqrt(144), giving a tangent length of 12 cm.

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