Arc Length

1
Arc Length

• the ratio of the length of an arc to the
  circumference is equal to the ratio of the
  measure of the arc to 360º

2
Example 1

• Find the length of arc AB to the nearest
  hundredth.

A
90º
B
15 ft
A ? 23.55 ft
3
Example 2

• Find the length of arc AB to the nearest
  hundredth.

A
40º
B
6 m
A ? 4.19 m
4
Example 3

• Find the measure of arc AB to the nearest degree.

A
18.84 m
B
9 m
mAB 120º
5
Example 4

• Find the radius of circle N to the nearest foot.

A
1.57 ft
45º
B
N
r 2 ft
6
Example 5

• Find the circumference of circle Q.

A
41.87 cm
Q
200º
B
C 75.37 cm
7
Unit 9 Acc. Alg/Geo A
Segment Theorems
8
Intersecting Chords Theorem
Interior segments are formed by two intersecting
chords.
Theorem
If two chords intersect within a circle, then the
product of the lengths of the parts of one chord
is equal to the product of the lengths of the
parts of the second chord.
a
d
b
c
a b c d
9
Intersecting Secants/Tangents
Exterior segments are formed by two secants, or a
secant and a tangent.
Secant and a Tangent
Two Secants
10
Intersecting Secants Theorem
If two secant segments are drawn to a circle from
an external point, then the products of the
lengths of the secant and their exterior parts
are equal.
a e c f
11
Example
AB ? AC AD ? AE
4 cm
4 ? 10 2 ? (2x)
6 cm
2 cm
40 4 2x
x
36 2x
X 18 cm
12
Secant and Tangent Theorem
The square of the length of the tangent equals
the product of the length of the secant and its
exterior segment.
a2 b d
a
b
c
d
13
Example
x
9 cm
25 cm