Radius of Circle with Parallel Chords

CAT 2019 Slot 1 · QA · Easy · Geometry

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In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

  1. A.

    13\sqrt{13}

  2. B.

    14\sqrt{14}

  3. C.

    11\sqrt{11}

  4. D.

    12\sqrt{12}

Answer

A

Explanation

Half chord lengths are 2 cm and 3 cm. Let distance of the 6 cm chord from centre be dd. Distance of the 4 cm chord from centre is d+1d + 1. Radius squared R2=d2+32=d2+9R^2 = d^2 + 3^2 = d^2 + 9. Also R2=(d+1)2+22=d2+2d+1+4=d2+2d+5R^2 = (d + 1)^2 + 2^2 = d^2 + 2d + 1 + 4 = d^2 + 2d + 5. d2+9=d2+2d+5⇒2d=4⇒d=2d^2 + 9 = d^2 + 2d + 5 \Rightarrow 2d = 4 \Rightarrow d = 2. R2=22+9=13⇒R=13R^2 = 2^2 + 9 = 13 \Rightarrow R = \sqrt{13}.

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