A chord of a circle is equal to its radius. Find the angle subtended by this chord on any point in the major segment.

Given a chord of a circle is equal to its radius.

In ΔOAB,

⇒ AB = OA = OB.

∴ ΔOAB is an equilateral triangle.

Each angle of an equilateral triangle is 60°.

∴ ∠AOB = 60°

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

⇒∠ACB = 1/2 ∠AOB = 1/2 (60°) = 30°

∴ Angle subtended by this chord at a point on the major arc is 30°.