Multiple choice

The centres of two circles with radii 8 cm and 3 cm are 13 cm apart. A direct common tangent touches the circle at A and B respectively then the length of AB is

  1. 8 cm

  2. 10 cm

  3. 12 cm

  4. 14 cm
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C Correct answer
Explanation

Length of direct common tangent = sqrt(d^2 - (R-r)^2) = sqrt(13^2 - (8-3)^2) = sqrt(169 - 25) = sqrt(144) = 12.

AI explanation

The formula for the length of a direct common tangent is the square root of the distance between centers squared minus the difference of the radii squared. Substituting the given values gives the square root of (13 squared minus (8 minus 3) squared). This simplifies to the square root of (169 minus 25), so the length of AB is 12 cm.

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