Hello, I need some help again. I need analgebraicproof of this theorem:

The perpendicular bisector of a chord of a circle passes through the center of the circle.There are plenty of geometric proofs out there, but I need one that just makes use of the midpoint formula and the Pythagorean theorem. I am just having some conceptual difficulty because I do not know how you prove that a point is on a certain line. I think I should show that the midpoint of the perpendicular bisector equals the midpoint of the diameter, but I don't know how to get a diameter. If someone could outline the basic steps you might use, I would really appreciate it!