Arcs and Chords Recognize and use relationships between

Arcs and Chords • Recognize and use relationships between arcs and chords. • Recognize and use relationships between chords and diameters. Each groove in a round waffle iron is the chord of a circle.

ARCS AND CHORDS The endpoints of a chord are also the endpoints of an arc.

Theorem In a circle or in adjacent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

The chords of adjacent arcs can form a polygon. Quadrilateral ABCD is an inscribed polygon because all of its vertices lie on a circle. Circle E is circumscribed about the polygon because it contains all of the vertices of the polygon. A D E C B

DIAMETERS AND CHORDS Diameters that are perpendicular to chords create special segment and arc relationships.

Theorem In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.

Example 1 Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD, which is 24 inches long. Radius Perpendicular to a Chord C B X a) If m. CD = 134, find m. CB O D

Example 1 Circle O has a radius of 13 inches. Radius OB is perpendicular to chord CD, which is 24 inches long. Radius Perpendicular to a Chord C B X a) If m. CD = 134°, find m. CB O b) Find OX D

Example 2 Chords AC and DF are equidistant from the center. If the radius of circle G is 26, find AC and DE. Chords Equidistant from Center F A B C E G D