A chord is a segment that joins two points of a circle.

 A diameter is a chord that contains the center of the circle.

 In a circle, a radius perpendicular to a chord bisects the chord. Converse: In a circle, a radius that bisects a chord is perpendicular to the chord. Also stated: In a circle, the perpendicular bisector of a chord passes through the center of the circle Extended form: In a circle, a diameter perpendicular to a chord bisects the chord and its arc.
 Proof:
Proof of the converse is left as an exercise.

 In a circle, or congruent circles, congruent chords are equidistant from the center. Converse: In a circle, or congruent circles, chords equidistant from the center are congruent.
 Proof:
Proof of the converse is left as an exercise.

 In a circle, or congruent circles, congruent chords have congruent arcs. Converse: In a circle, or congruent circles, congruent arcs have congruent chords.
 Proof:
Proof of the converse is left as an exercise.

 In a circle, parallel chords intercept congruent arcs
 Proof: