12-2 Arcs and Chords

A chord always cuts a circle into two arcs, usually a minor and major. -a segment whose endpoints are on a circle. A chord always cuts a circle into two arcs, usually a minor and major. We speak of as being the arc of chord

Theorem: In the same circle, or congruent circles: (1) Congruent central angles have congruent arcs (2) Congruent arcs have congruent central angles

Theorem: In the same circle, or congruent circles: (1) Congruent central angles have congruent chords (2) Congruent chords have congruent central angles

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

We can have midpoints of arcs, they act just like midpoints of segments.

Works with radii as well.

Find x and y.

Find the length of a chord that is a distance of 7 inches from the center of a circle with a radius of 11.

is 15 and PR = 9