A chord of a circle is equal to the radius of the circle. Find the angle subtended by thre chord at a point on the minor arc and also at a point on the major arc.

Given that: A chord of a circle equal to its radius, So,

In ,

AB = OA = OB = radius of circle

Thus,  is an equilateral triangle

Therefore, each interior angle of this triangle will be of  

So,

And, 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.

In cyclic quadrilateral ACBD,

Therefore, angle subtended by the chord at a point on the major arc is and on minor arc is

 

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