Question

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

(a) 10 cm
Let the radius of the circle be r cm.
Let OD = OB = r cm.
Then OE = (r - 4) cm and ED = 8 cm
Now, in right ΔOED, we have:
OD² = OE² +ED²
⇒ (r)² = (r - 4)² + 8²
⇒ r² = r² + 16 - 8r + 64
⇒ 8r = 80
⇒ r = 10 cm
Hence, the required radius of the circle is 10 cm.