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

Question

Philoid · Accepted Answer

Let AB be the chord of the circle with center O.

Given that AB = Radius of the circle.

Also, AO = BO = Radius

∴ ΔOAB is an equilateral triangle.

Thus, ∠AOB = ∠OBA = ∠OAB = 60°

Also, angle subtended by an arc at the center of the circle is twice the angle subtended by it at any other point in the remaining part of the circle.

∴ ∠AOB = 2∠ACB

⇒ ∠ACB = 1/2 (∠AOB)

⇒ ∠ACB = 1/2 (60°) = 30°