In the given figure, a circle with center is given in which a diameter bisects the chord at a point such that and Find the radius of the circle.

Question

Philoid · Accepted Answer

Let radius OA = OB = OD = r

DE = 8 cm

OE = OB – BE

⇒ OE = r – 4

In triangle ODE,

OD² = DE² + OE²

⇒ r² = 8² + (r - 4)²

⇒ r² = 64 + r² + 16 - 8r

⇒ 8r = 80

⇒ r = 10 cm

Hence, radius of circle = 10 cm.