Question

9. In the given figure, O is the centre of a circle
and diameter AB bisects the chord CD at a point
E such that CE = ED = 8 cm and EB = 4 cm. The
radius of the circle is
(a) 10 cm
(b) 12 cm
(c) 6 cm
(d) 8 cm​

Answer 1

Answer:

a) 10 cm

Step-by-step explanation:

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.