Chords and Arcs

1
Section 11-2

• Chords and Arcs

2
Chord

• Chord-segment whose endpoints are on a circle

3
Theorem 11-4

• Within a circle or in congruent circles
• Congruent Central angles have congruent chords.
• Congruent chords have congruent arcs
• Congruent arcs have congruent central angles

1) BC CD
BC CD
B
C
50
50
A
D
4

• Find x

If ?ADE ? ?BDE and?ADE 52?
What is the measure ofarc AE?
52
What is the measure ofarc AB?
104
5
Theorem 11-5

• Within a circle or in congruent circles
• Chords equidistant from the center are congruent
• Congruent chords are equidistant from the center.

A
B
90
90
D
C
6
Using theorem 11-5

• Find X

Since the chords are the same distance from the
center the chords are congruent
x
90
X 12
90
12
7
Theorem 11-6

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

DB is the diameter
A
AE EC
D
B
E
AB BC
C
8
Theorem 11-7

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

If DB is a diameter,
A
Then DB - AC.
D
B
E
C
9
Theorem 11- 8

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

A
DB must contain the center, and is therefore a
diameter of the circle.
D
B
E
C
10
Applying theorems

• Find X

Since the chord is perpendicular to the diameter
it is bisected.
3² 4² x²
9 16 x² 25 x² 5 x
A
x
3 in.
8 in.
11
Homework

• Page 593
• Problems 4-7,9,10,12,13,16-18