Multiple choice

The distance between the centres of two circles is 61 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?

  1. 60

  2. 54

  3. 48

  4. 72
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A Correct answer
Explanation

The length of the direct common tangent is given by sqrt(d^2 - (R-r)^2), where d is the distance between centers and R, r are the radii. Here, sqrt(61^2 - (35-24)^2) = sqrt(3721 - 121) = sqrt(3600) = 60.

AI explanation

The length of the direct common tangent to two circles is found using the formula L equals the square root of the quantity (d squared minus r1 squared minus r2 squared), where d is the distance between centers. Substituting the given values, L equals the square root of the quantity (61 squared minus 35 squared minus 24 squared). This simplifies to the square root of the quantity (3721 minus 1225 minus 576), which is the square root of 3600, giving a length of 60 cm.

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