Question

Prove perpendicular bisector of a chord of a circle contains the center of the circle

Answer 1

Answer:

The perpendicular bisector of any chord of any given circle must pass through the center of that circle. ... From this it is manifest that, if in a circle a straight line cut a straight line into two equal parts and at right angles, the centre of the circle is on the cutting straight line.The perpendicular bisector of a chord passes through the center of a circle. Since is the center of the given circle, because both of them are radii of the same circle. Also, since is the midpoint of . In addition, because a segment is congruent to itself