# In a circle, two parallel chords on the same side of a diameter

Geometry
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

- √12
- √14
- √13
- √11

### Answer

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 drawn 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 = √13

**The correct option is C.**