Multiple choice

$AB$ and $CD$ are two parallel chords of circle such that $AB = 10$ cm and $CD = 24$ cm. If $LM = 17$ cm, then the diameter of the circle is

  1. $13$ cm
  2. $26$ cm
  3. $14$ cm

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r be the radius. The distances from the center to the chords are d1 = sqrt(r^2 - 5^2) and d2 = sqrt(r^2 - 12^2). Since chords are on the same side, d1 - d2 = 17 (or d1 + d2 = 17). Solving sqrt(r^2 - 25) - sqrt(r^2 - 144) = 17 leads to r = 13. Diameter = 2r = 26.

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