Prove that the hypotenuse of a Euclidean right triangle is a diameter of the circumscribed circle.

Given theorem: Let $\displaystyle \triangle{ABC}$ be a triangle and let M be the midpoint of segment AB. If $\displaystyle \angle{ACB}$ is a right angle, then AM = MC.

I've drawn a diagram to help me but don't know where to begin on the proof.