Question

7. 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 = 8 cm and EB = 4 cm.
Find the radius of the circle.10​

Answer 1

Let the radius of a circle be x

So, OC=OD=x

As, OB=OE+EB

x=OE+4 [Since Ob is the radius and EB=4 cm given]

OE=x−4

We know that if a line drawn from the centre to the chord bisects the chord, then it is perpendicular to the chord

Hence, OE⊥CD

In △OED

OE

2

+ED

2

=OD

2

(x−4)

2

+8

2

=x

2

x

2

+16−8x+64=x

2

−8x+80=0

8x=80

x=10 cm

Thus, radius of the circle is 10 cm

Answer 2

Let the radius of a circle be x

So, OC=OD=x

As, OB=OE+EB

x=OE+4 [Since Ob is the radius and EB=4 cm given]

OE=x−4

We know that if a line drawn from the centre to the chord bisects the chord, then it is perpendicular to the chord

Hence, OE⊥CD

In △OED

OE

2

+ED

2

=OD

2

(x−4)

2

+8

2

=x

2

x

2

+16−8x+64=x

2

−8x+80=0

8x=80

x=10 cm

Thus, radius of the circle is 10 cm.