Question

prove that the angle subtended at the centre of a circle is bisected by the radius passing through the midpoint of the arc

Answer 1

let the angle subtended by the arc at the center be x . So the length of the arc is (2×pi×r×x)/360
Now the radius passes through midpoint of arc
So the length half of the arc is
((2×pi×r×x)/360)×1/2
or 2×pi×r×(x/2)×360
Thus we see that the angle subtended at the centre of a circle is bisected by the radius passing through the midpoint of the arc

Answer 2

Answer:

let the angle subtended by the arc at the center be x . So the length of the arc is (2×pi×r×x)/360

Now the radius passes through midpoint of arc

So the length half of the arc is

((2×pi×r×x)/360)×1/2

or 2×pi×r×(x/2)×360

Thus we see that the angle subtended at the centre of a circle is bisected by the radius passing through the midpoint of the arc