11-2Chords and Arcs

Theorems: 11-4, 11-5, 11-6, 11-7, 11-8Vocabulary: Chord

Vocabulary

Chord A segment whose endpoints are on a circle.

chord a is PQP

O

Q

Theorem 11-4

Within a circle or in a congruent circles:

1. Congruent central angles have congruent chords.

2. Congruent chords have congruent arcs.

3. Congruent arcs have congruent central angles.

B

O

DFBC

#1 Using Theorem 11-4

C

F

D

P

, Given that PO : then, and DFBC

PO

Theorem 11-5

Within a circle or in a congruent circles:

1. Chords equidistant from the center are congruent.

2. Congruent chords are equidistant from the center.

#2 Using Theorem 11-5

x

18

18

1818x

36x

Theorem 11-6

In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs.

Theorem 11-7

In a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord.

Theorem 11-8

In a circle, the perpendicular bisector of a chord contains the center of the circle.

#3 Using Diameters and Chords

46.8

x

222 8.64 y

y

24.4616 2 y

24.302 y

5.524.30 y

5.52x

11x