Question

a chord of 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

Answer 1

okay
the chord of circle = radius of circle
which makes an equilateral triangle
- we know that the sum or all the angles of an equilateral triangle is 60 degree.
so angle AOC =60
Angle ABC =1/2 of angle AOC
( angles subtended by an arc at the centre is double of any other angle at the circle)
there fore , angle ABC = 1/2 AOC
=30
Now, angle ABC +angle ARC =180 (angles of cyclic quadrilatral)
- 30 +angle ARC =180
- angle ARC = 180-30
=150
At major arc angle ABC =30
At minor arc angle ARC=150
Don't forget to use degree!!!!!