Question

The radius of a circle is 8 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.

Answer 1

Radius of circle (OA) = 8 cm   ......(Given)

Chord (AB) = 12cm                .......(Given)

Draw a perpendicular OC on AB.

We know, perpendicular from centre to chord bisects the chord

Which implies, AC = BC = `12/2` = 6 cm

In right ΔOCA:

Using Pythagoras theorem,

OA² = AC² + OC²

64 = 36 + OC²

OC² = 64 – 36 = 28

or OC = √28 = 5.291 (approx.)

The distance of the chord from the centre is 5.291 cm.