Arcs and Chords:

Theorem:

In congruent circles or in the same circle:
1. Congruent arcs have congruent chords.
2. Congruent chords have congruent arcs.

Theorem:

A diameter that is perpendicular to a chord bisects that chord and the arc in the chord.

Theorem:

In congruent circles or in the same circles:
1. Chords that are equally distant from the center (or centers) are congruent.
2. Congruent chords are equally distant from the center (or centers).a