Question
Prove that the number of radians in an angle subtended by an arc of a circle at the centre =
Solution
Draw a circle of radius OA = r with centre at O.
Cut off an arc AB of length r and join OB; then radian.
Cut off an another arc ABC of length l and join OC such that (radians). Since angles at the centre of the circle are proportional to the arcs on which they stand,
∴