It frustrates me to be presented with a formula in a math book, but there is no proof to show that it is true.

Does anyone have proofs for the following?

The length of an arc of a circle, s, subtended by a central angle, theta, and a radius, r is: theta = s/r -- how to prove this?

How to prove that the circumference of a circle = 2*pi*r

How to prove area of circle = pi*r^2

Thanks