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

Answer 1

AB is the diameter of the circle with centre O, which bisects the chord CD at point E.
Given: CE = ED = 8 cm and EB = 4 cm
Join OC.

Let OC = OB = r cm (Radii of a circle)
Then OE = (r − 4) cm
Now, in right angled ΔOEC, we have:
OC² = OE² + EC² (Pythagoras theorem)
⇒ r² = (r − 4)² + 8²
⇒ r² = r² − 8r + 16 + 64
⇒ r² − r² + 8r = 80
⇒ 8r = 80
⇒r=808 cm=10 cm
⇒ r = 10 cm
Hence, the required radius of the circle is 10 cm.