Question

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Answer 1

We have, OA = OB = AB 

Therefore, ∆OAB is a equilateral triangle. 

⇒ ∠AOB = 60° 

We know that angle subtended by an arc at the centre of a circle is double the angle subtended by the same arc on the remaining part of the circle. 

∴ ∠AOB = 2∠ACB 

⇒ ∠ACB = 1/ 2 ∠AOB = 1/ 2 × 60° 

⇒ ∠ACB = 30° 

Also, ∠ADB = 1/ 2 reflex ∠AOB 

= 1/ 2 (360° – 60°) = 1/ 2 × 300° = 150° 

Hence, angle subtended by the chord at a point on the minor arc is 150° and at a point on the major arc is 30° Ans