1. 10-6 Circles & Arcs
Lesson 10-6 GQ:

2. A CIRCLE is the set of all points equidistant from a given point called the center .;
A B E AB AC
radius
diameter
Circle B
radius
diameter

3. Types of Angles Central angle Inscribed angle
- the vertex is on the center.
Inscribed angle
- the vertex is on the circle.

4. Types of Arcs Major arc Minor arc Semicircle P M O N or MN
- the measure is more than 180 °
Example: MNO P
- the measure is less than 180 °
Example: MO O
- the measure is equal to 180 ° N
or MN
Example: MON

5. Measure of Arcs & Angles
In a circle, the measure of the central angle is always equal to the measure of its intercepted arc.
x = n
m ∠ ABC = m AC n° C
If ∠ ABC is 80°, what is the measure of arc AC? A x°
B °
m AC = 80°

6. Measure of Arcs & Angles
EXAMPLE: In the diagram below, if the m ∠ xyz is 68°, find the measure of a.) minor arc and b.) major arc.
SOLUTION:
a. measure of minor arc
m ∠xyz = m xz (since ∠xyz is a central angle) x
m xz = 68°
b. measure of major arc
major arc = 360° – m xz (minor arc)
68°
=360° – 68°
m xz (major arc) = 292°
68° y
292° z

7. The distance around a circle
THM 10-9: Circumference
The distance around a circle or

8. Find the circumference to the nearest tenth.1. 2.
33 m
14.3 in.
C = 89.8 in
C = m
Exact
answer:
in terms
of pi

9. a fraction of the circumference of a circle
Arc Length
a fraction of the circumference of a circle
piece
portion
part
section

10. THM 10-10: Arc Length THM
the ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to 360º

11. EX1: Find the length of arc AB to the nearest hundredth.
90º B
15 ft
A  ft

12. Ex2: Find the measure of arc AB to the nearest degree.
mAB = 120º

13. Ex3: Find the circumference of circle Q.A
41.87 cm Q
200º B
C ≈ cm