9-3Arcs and Chords

Objectives:• To recognize and use relationships among arcs, chords,

and diameters.

Vocabulary

• Arc of the Chord• Inscribed Polygon

Arc of the Chord

• When a minor arc and a chord share the same endpoints we call the arc, the arc of the chord.

Inscribed Polygon

• A polygon is an inscribed polygon if each of vertices lies on the circle.

Theorem 9-1

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

Example 1• Find

Theorem 9-2

• In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.

Example 2

• Find

Theorem 9-3

• In a circle or in congruent, two chords are congruent if and only if they are equidistant from the center.

Example 3• Find