Question

If the chord of a circle is equal to the radius of the circle, then the angle subtended by the chord at a point on the minor arc is:

Answer 1

It is given that the chord is equal to radius of the circle.
It means if we join both ends of the chord with the center of the circle,
it will create an equilateral triangle.
`/_AOB = 60^@`
Here, `AB` is the chord and `O` is the center of the circle.
Please refer to video for the figure.
Now, we know that angle subtended at the center by a chord is double of that of angle created at any point on the circle.
`:. /_AOB = 2/_ACB =>/_ACB = 1/2/_AOB = 30^@`
Also, sum of opposite angles of a cyclic quadrilateral is `180^@`.
`:. /_ACB+/_ADC = 180^@`
`:./_ADC = 180-30 = 150^@`
So, angle created by the minor arc is `150^@`.