Question

' prove that the anglesubtended at the centre of a circle is bisected by the radius passing through the mid point of the arc

Answer 1

let us suppose that the radius passes through the mid point without bisecting the angle.

By the formula for length of an arc
$l(arc) = \frac{ \alpha }{360} \times 2\pi \times r$

here alpha is angle subtended and r is radius
if length of arc of both part is same then angle subtended is same since radius ,π are constant