# Is there a proof that a perpendicular bisector of a chord passes through the center of it's circle?

It seems intuitive because any line perpendicular to the circle passes through the center of the circle, and a chord is just a tangent line translated into the circle. So is this part of the definition of a circle?

Specifically, what brings to mind this is the construction of the center given an arbitrary circle. Two chords and their perp bisectors should work, but how would I prove that's true?

Because the perpendicular bisector of a chord $AB$ it's the locus of points $M$, for which $MA=MB$.
Since by definition all locus is a set of all point with a common property and $OA=OB$, then $O$ must be placed on the perpendicular bisector of the chord.
Here $O$ is a center of the circle.