Multiple choice

[CAT 2005] What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?

  1. 1 or 7

  2. 2 or 14

  3. 3 or 21

  4. 4 or 28
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D Correct answer
Explanation

Distance from center to chord of length 32 is d1 = sqrt(20^2 - 16^2) = 12. Distance from center to chord of length 24 is d2 = sqrt(20^2 - 12^2) = 16. If chords are on the same side, distance = |16 - 12| = 4. If on opposite sides, distance = 16 + 12 = 28.

AI explanation

A perpendicular drawn from the center of a circle to a chord bisects the chord. For the chord of length 32 cm, the perpendicular distance from the center is calculated using the Pythagorean theorem as the square root of (20 squared minus 16 squared), which is 12 cm. For the chord of length 24 cm, the distance is the square root of (20 squared minus 12 squared), which is 16 cm. The distance between the two parallel chords is the sum or difference of these distances from the center, yielding 16 + 12 = 28 cm or 16 - 12 = 4 cm.

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