Question

The given figure shows a circle centred at O in which the
diameter AB bisects the chord CD at point E. If CD=16 cm and EB=4 cm, then find the radius of the circle.

Answer 1

• Given: AB bisects the chord CD at point E, i.e., OE bisects the chord CD.

Construction

• Join OD.

We know that, The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.​

∴ OE ⊥ CD

ED = EC = 16/2 cm = 8 cm

Let ‘r’ be the radius of the circle.

OD = OB = r cm

OE = OB − EB = (r − 4) cm

In △OED,

By Pythagoras theorem,

OD2 = OE2 + ED2

r2 = (r − 4)2 + 82

∴ r2 = r2 − 8r + 16 + 64

∴ 8r = 80

∴ r = 10 cm

Hence, radius r = 10 cm.