Question

Fill In The Blanks

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

Answer 1

Given:
A chord of a circle is equal to its radius

Let AB is a chord and O is the centre of the circle.

AB = OA = OB (∵ Chord is equal to the radius)
⇒ ∆ABO is equilateral triangle

Thus, ∠AOB = 60° ...(1)


We know, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
Thus, ∠AOB = 2∠ADB , where D is any point on the major segment of the circle
⇒ 2∠ADB = 60° (from (1) and (2))
⇒ ∠ADB = 30°

Hence, the angle subtended by the chord at a point in major segment is 30°.