# Arcs and Chords

Document Sample

```					  Lesson 8-4

Arcs
and Chords
Lesson 8-4: Arcs and Chords   1
Theorem #1:
In a circle, if two chords are congruent then their corresponding
minor arcs are congruent.
A           B
If AB  CD then AB  CD                                E

C
D
Example:   Given mAB  127 , find the mCD.

Since mAB  mCD
mCD  127
Lesson 8-4: Arcs and Chords           2
Theorem #2:
In a circle, if a diameter (or radius) is perpendicular to a
chord, then it bisects the chord and its arc.
If DC  AB then DC bi sec ts AB and AB.
 AE  BE and AC  BC                                    D

Example: If AB = 5 cm, find AE.                          A       E       B

If mAB  120 , find mAC.                           C
AB       5
AE          AE   2.5 cm
2       2
m AB            120
m AC       ,  m AC       60
2              2
Lesson 8-4: Arcs and Chords               3
Theorem #3:
In a circle, two chords are congruent if and only if
they are equidistant from the center.            D
F

CD  AB iff OF  OE
C
O

A       E       B
Example:   If AB = 5 cm, find CD.

Since AB = CD, CD = 5 cm.

Lesson 8-4: Arcs and Chords               4
Try Some Sketches:
 Draw a circle with a chord that is 15 inches long and 8 inches from
the center of the circle.
 Draw a radius so that it forms a right triangle.

 How could you find the length of the radius?

Solution: ∆ODB is a right triangle and OD bi sec ts AB
AB 15
DB=      = =7.5 cm                                  A   15cm
B
2    2                                            D
OD=8 cm                                                     8cm       x
OB2 =OD2 +DB2                                           O

OB2 =82 +(7.5) 2 =64+56.25=120.25
OB= 120.25  11cm

Lesson 8-4: Arcs and Chords                 5
Try Some Sketches:
 Draw a circle with a diameter that is 20 cm long.
 Draw another chord (parallel to the diameter) that is 14cm long.

 Find the distance from the smaller chord to the center of the circle.
AB 14
Solution: OE bi sec ts AB.  EB            7cm
2    2
∆EOB is a right triangle. OB (radius) = 10 cm A         14 cm
B
OB 2  OE 2  EB 2                                  E
x
10 cm
10  X  7
2     2    2                                                        10 cm
C      20cm   O           D

X 2  100  49  51
X  51  7.1 cm
Lesson 8-4: Arcs and Chords                 6

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 1 posted: 7/27/2012 language: pages: 6