Question

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

Answer 1

Given, AB is a chord of a circle, which is equal to the radius of the circle,

i.e., AB = BO  ...(i)

Join OA, AC and BC.

Since, OA = OB = Radius of circle

OA = AS = BO

Thus, ΔOAB is an equilateral triangle.

⇒ ∠AOB = 60°  ...[Each angle of an equilateral triangle is 60°]

By using the theorem, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.

i.e., ∠AOB = 2∠ACB

⇒ ∠ACB = `60^circ/2` = 30°