# 11-2 Chords and Arcs

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```					11-2
Chords and Arcs

Theorems:
11-4, 11-5, 11-6, 11-7, 11-8
Vocabulary:
Chord
Vocabulary
   Chord                A segment whose
endpoints are on a
circle.

Q
P
O
PQ is a chord
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.
#1 Using Theorem 11-4

Given that O  P,          B

and BC  DF , then :   O

C

O  P                    D

P

BC  DF                       F
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
x  36         18

x
18
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

4  y  6.8
2        2       2

16  y  46 .24
2

y  30 .24
2

6.8
4
y  30 .24  5.5         y   x

x  25.5
x  11

```
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