In the given figure, the diameter of a circle with center is perpendicular to chord If and calculate the radius of the circle.

Question

Philoid · Accepted Answer

Let radius OA = OC = OD = r

Chord AB = 12 cm

OE = OC – CE

⇒ OE = r – 3

AE = (1/2) AB

⇒ AE = (1/2) 12 = 6 cm

In triangle AOE,

OA² = AE² + OE²

⇒ r² = 6² + (r - 3)²

⇒ r² = 36 + r² + 9 - 6r

⇒ 6r = 45

⇒ r = 7.5 cm

Hence, radius of circle = 7.5 cm.