prove perpendicular bisector of the chord of a circle goes though the origin

Hi

Can you show me how to prove that the perpendicular bisector of a chord goes through the origin, or from another perspective, that if a line bisects a chord and goes through the origin it is perpendicular to the chord. I have looked for examples on the internet that describe how to do this but they all use something called the perpendicular bisector theorem. I have not covered this yet in my book. This is just the beginning of a basic geometry section.

I saw this example here
http://hrsbstaff.ednet.ns.ca/macdonaz/MatA12/Pg%20219-202%20Q29-32%20Answers.pdf

and i understood it up to this line m (angle) CMA

I don't know what the notation with the little m means. I also don't know the rule used in this angle that 2 angles that are supplementary and complementary must both be 90 degrees.

I guess the problem is explaining it using proofs that I have covered and y ou don't know what I do and don't know yet!

Many thanks