Consider a circle of radius r.
a. (i) Starting only with the definition of one radian, prove that the angle subtended by a complete circle is 2π radians.
b. (ii) Hence derive a general relation between the length of an arc, the radius of the circle, and the angle subtended by that arc at the centre (express the angle in radians).
c. (iii) A wheel of radius 20cm makes 75 complete revolutions. Using the relation obtained in part (ii), determine the total distance travelled by a point on the rim of the wheel.