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

  1. √12
  2. √14
  3. √13
  4. √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.

r2 = x2 + 32 = (x + 1)2 + 22

Solving,

x = 2 and r = √13

The correct option is C.