CAT 2018 Slot 1 QA Question 19: 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

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

Accepted Answer

The longer chord is closer to the centre. Let its perpendicular distance from the centre be d.
Then the perpendicular distance of the shorter chord from the centre is $d + 1$.
Half-lengths of the chords are 3 cm and 2 cm respectively.
$r^{2} = d^{2} + 3^{2}$
$r^{2} = (d + 1)^{2} + 2^{2}$
$d^{2} + 9