A chord of a length 30 cm is drawn at a distance of 8 cm from the center of a circle. Find out the radius of the circle.

Question

Philoid · Accepted Answer

Let distance OC = 8 cm

Chord AB = 30 cm

Draw OCAB

Therefore,

OC bisects AB at C

AC = (1/2) AB

⇒ AC = (1/2) 30

⇒ AC = 15 cm

In triangle OCA,

OA² = OC² + AC²

⇒ OA² = 8² + 15²

⇒ OA²= 64 + 225

⇒ OA²= 289

⇒ OA = 17 cm

Hence, radius of the circle = 17 cm.