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