Equal chords of a circle subtend equal angles at the center and its converse. The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord. There is one and only one circle passing through three given non-collinear points. Equal chords of a circle are equidistant from the center and conversely. Angles in the same segment of a circle are equal.
