Is it possible to construct the center of a circle from a single chord?
If I construct the perpendicular bisector of the chord and then construct the perpendicular bisector of that, wouldn't the exact point of intersection be the center of the circle?
We have the basic theorem in Euclidean geometry: when we have a cord in a circle (= a line segment joining two distinct points of a circle), then the cord's perpendicular bisector passes through the circles center (the other direction is also true, so this is an iff theorem). Thus, as I noted in my first comment, if the cord's perp. bisec. is made into a cord (meaning: take the segment of the perp. bis. joining two different points on the circle), it is always a diameter