You can put this solution on YOUR website! Proving the circumference of a circle is is a little tricky using a two-column proof. It's also difficult to construct a proof of the circumference without using calculus.
The best way is to consider a regular n-sided polygon and its perimeter. Suppose the distance from the center of an n-sided polygon to one of its vertices is (where is constant). We can construct isosceles triangles, each one looking something like this:
where . Hence, the base of the isosceles triangle is (applying the definition of sine). We have n of these segments so the perimeter of the n-gon is
