1. 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.

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

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

4. A B D E C 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 B E C

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

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

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

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

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