Multiple choice

SR is a direct common tangent to the circles of radii 8 cm and 3 cm, respectively; their centres being 13 cm apart. If the points S and R are the respective points of contact, then the length of SR is

  1. 12 cm

  2. 11 cm

  3. 17 cm

  4. 10 cm
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A Correct answer
Explanation

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

AI explanation

Draw a line from the center of the smaller circle parallel to the tangent SR until it meets the radius of the larger circle at the point of tangency. This forms a right-angled triangle with a hypotenuse of 13 cm (the distance between centers) and a base of 5 cm (8 cm minus 3 cm). Using the Pythagorean theorem, the height SR equals the square root of (13 squared minus 5 squared), which is the square root of 144. The length of SR is 12 cm.

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