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

Explanation

The chord `AB` is equal to the radius of the circle.

`OA` and `OB` are the two radii of the circle.
From `triangleOAB`.
`AB = OA = OB =` radius of the circle.
` triangleOAB` is an equilateral triangle.

`therefore AOC = 60^@`
And, `ACB = 1/2 AOB`
So, `ACB =1/2 xx 60^@ = 30^@`
Now,
`ACBD` is a cyclic quadrilateral,
`ADB +ACB = 180^@` (Since they are the opposite angles of a cyclic quadrilateral)
So, `ADB = 180^@-30^@ = 150^@`
So, the angle subtended by the chord at a point on the minor arc and also at a point on the major arc is `150^@` and `30^@`respectively.