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CAT 2018 [SLOT 1] Quant Question with Solution 07

Question:
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. \(\sqrt {12} \)
  2. \(\sqrt {14} \)
  3. \(\sqrt {13} \)
  4. \(\sqrt {11} \)
Show Answer
Correct Answer: 3

Let the 6 cm long chord be x cm away from the centre of the circle. Let the radius of the circle be r cm.

The perpendiculars from the centre of the circle to the chords bisect the chords.

$r^{2}=x^{2}+3^{2}=(x+1)^{2}+2^{2}$

Solving, $x=2$ and $r=\sqrt{13}$


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