1. How do we use angle measures to find measures of arcs?
CCGPS Geometry
UNIT QUESTION: What special properties are found with the parts of a circle?
Standard: MMC9-12.G.C.1-5,G.GMD.1-3
Today’s Question:
How do we use angle measures to find measures of arcs?
Standard: MMC9-12.G.C.2

2. AGENDA
Notes on Circles
Notes on Central Angles
Homework Worksheet

3. Unit 3
Circles

4. Segments
of Circles

5. Parts of a Circle
Circle – set of all points _________ from a given point called the _____ of the circle.
equidistant C
center
Symbol: C

6. CHORD:
A segment whose endpoints are on the circle

7. Radius
RADIUS:
Distance from the center to point on circle P

8. Distance across the circle through its center
Diameter
DIAMETER:
Distance across the circle through its center P
Also known as the longest chord.

9. D = ? 24 32 12
r = ? 16
r = ?
4.5 6
D = ? 12 9

10. Use P to determine whether each statement is true or false.Q R T S
True: thumbs up False: thumbs down

11. Secant Line:
intersects the circle at exactly TWO points

12. a LINE that intersects the circle exactly ONE time
Tangent Line:
a LINE that intersects the circle exactly ONE time
Forms a 90°angle with a radius
Point of Tangency: The point where the tangent intersects the circle

13. Secant Radius Diameter Chord Tangent
Name the term that best describes the notation.
Secant
Radius
Diameter
Chord
Tangent

14. Central
Arcs

15. Central Angle : An Angle whose vertex is at the center of the circle
Major Arc
Minor Arc
More than 180°
Less than 180°
ACB P AB
To name: use 3 letters C
To name: use 2 letters B
APB is a Central Angle

16. Semicircle: An Arc that equals 180°
To name: use 3 letters E D
EDF P F

17. THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal

18. measure of an arc = measure of central angle
96 Q
m AB =
96° B C
m ACB =
264°
m AE =
84°

19. Arc Addition PostulateB
m ABC =
+ m BC
m AB

20. 240 260 m DAB = m BCA = Tell me the measure of the following arcs. D
140
260
m BCA = R
40
100
80 C B

21. CONGRUENT ARCS
Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B D 45 45
110 A
Arc length is proportional to “r”

22. Classwork
Practice Worksheet

23. Homework:
Practice Worksheet