Question

In the given figure, a circle with centre O is given in which a diameter AB bisects the chord CD at a point E such that CE = ED = 8cm and EB = 4cm. Find the radius of the circle.

Answer 1

Consider AB as the diameter with centre O which bisects the chord CD at E

It is given that

CE = ED = 8cm and EB = 4cm

Join the diagonal OC

Consider OC = OB = r cm

It can be written as

OE = (r – 4) cm

Consider △ OEC

By using the Pythagoras theorem

OC² = OE² + EC²

By substituting the values we get

r² = (r – 4)² + 8²

On further calculation

r² = r² – 8r + 16 + 64

So we get

r² = r² – 8r + 80

It can be written as

r² – r² + 8r = 80

We get

8r = 80

By division

r = 10 cm

Therefore, the radius of the circle is 10 cm.