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Distance between parallel chords

CAT 2005 Slot 1 · Quantitative Ability · Easy · Geometry

This is an easy Quantitative Ability question from the CAT 2005 Slot 1 paper. It tests Geometry. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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. A.

    1 or 7

  2. B.

    2 or 14

  3. C.

    3 or 21

  4. D.

    4 or 28

Answer

D

Explanation

Distance of chord of length 32 cm from center =202−162=12= \sqrt{20^2 - 16^2} = 12 cm. Distance of chord of length 24 cm from center =202−122=16= \sqrt{20^2 - 12^2} = 16 cm. Case 1: Both chords lie on the same side of the center. Distance =16−12=4= 16 - 12 = 4 cm. Case 2: Chords lie on opposite sides of the center. Distance =16+12=28= 16 + 12 = 28 cm. Thus, the distance can be 4 or 28 cm.

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