Q. 75.0( 3 Votes )

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

Answer :


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°.


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