The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is (a) `60^@` (b) `75^@` (c) `120^@` (d) `150^@`

Explanation

Given,`AB` is equal to the radius of the circle.
In `/_\OAB,OA=OB=AB=` radius of the circle.
Thus, `/_\OAB` is an equilateral triangle.
`/_AOC=60^@.`
Also, `/_ACB=1/2/_AOB=1/2xx60^@=30^@.`
Since, `ACBD` is a cyclic quadrilateral,
`/_ACB+/_ADB=180^@`(Opposite angles of cyclic quadrilateral are supplementary)
`/_ADB=180^@−30^@=150^@`
Thus, angle subtend by the chord at a point on the minor arc and also at a point on the major arc are `150^@ \and\ 30^@`, respectively.