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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. $\sqrt {11}$

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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