Arcs and Chords
Arc – Chord Theorem: In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Radius – Chord Theorem: In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc,
Converse of Radius – Chord Theorem: In a circle, a diameter bisects a chord and its arc if and only if it is perpendicular to the chord.
Chord – Distance Theorem: In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
Corollary: In a circle or in congruent circles, two chords are congruent if and only if their central angles are congruent.
Learn how to identify and use the relationships among arcs, chords, and diameters by reading the explanation below.
Practice: Answer the following exercises about arcs and chords.