1. 10.6
Circles & Arcs

2. 10.6 – Circles & Arcs Goals / “I can….”
Find the measures of central angles and arcs
Find circumference and arc length

3. 10.6 – Circles & Arcs
In a plane, a circle is the set of all points equidistant from a given point called the center.
You name a circle by its CENTER C P A B

4. 10.6 – Circles & Arcs
Radius – a segment that has 1 endpoint at the center and the other on the circle
Congruent circles have congruent radii
Diameter – segment that contains the center and has both endpoints on the circle
Central Angle – vertex is on the center C P A B

5. 10.6 – Circles & Arcs Other 15% Sleep 31% Food 9% Work 20%
Entertainment
18%
Food 9%
Must do 7%
Work
20%

6. 10.6 – Circles & Arcs An arc is part of a circle
A semicircle is HALF of a circle ( = 180°)
A minor arc is smaller than a semicircle ( < 180°)
A major arc is larger than a circle ( > 180°)

7. 10.6 – Circles & Arcs Identify the following in O Minor arcs
Semicircle
Major arcs that contain A A C B D O

8. 10.6 – Circles & Arcs Find the measure of the following arcs: BC BD
ABC AB
58° B D C O
32°

9. 10.6 – Circles & Arcs
Circumference of a circle:
C = πd or C = 2πr d r

10. 10.6 – Circles & Arcs
A car has a turning radius of 16.1 ft. The distance between the 2 front tires is 4.7 ft. How much farther do the outside tires travel than the inside tires? 16
4.7

11. 10.6 – Circles & Arcs
Arc length
AB = x 2πr
mAB
360 r B O A

12. 10.6 – Circles & Arcs
Find the length of the arcs: 16 X Y O X Y O