Key Concepts: Arcs and Chords

Congruent Arcs and Chords

In the same circle or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Theorems

• If a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.
• Two chords are congruent if and only if they are equidistant from the center.
• The perpendicular from the center to a chord bisects the chord.

Applications

• Use the Pythagorean Theorem with radius, half-chord, and distance from center to find missing lengths.