1. Warm-Up
The measurements of two vertical angles are 15x and 10x+15. What is the measurement of each angle?

2. Day 24 Circles: Vocab & Central Angles
Today’s Question: How do we use angle measures to find measures of arcs? (MMC9-12.G.C.2)

3. AGENDA Notes on Circles Notes on Central Angles Practice Worksheet
Homework Worksheet

4. Unit 3
Circles

5. Circle
The set of all points that are __________ from a reference point, the ________.
The set of points from a 2-dimensional curve that measures ___.
equidistant
center C
360
Symbol: C

6. CHORD:
A __________whose __________ lie on the circumference of the circle.
segment
endpoints

7. Diameter Also known as the longest chord. P
A straight line passing through the _______ of a circle connecting two points on the circle; equal to ______ the radius.
center
twice P
Also known as the longest chord.

8. Radius
The distance from the ______ to a ______ on the circle; equal to ____ the diameter.
center P
point
half

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: A line that intersects a circle at exactly _____ points.
TWO

12. Tangent Line:
a LINE that intersects a circle at exactly ____ point and is ____________ to the radius of the circle.
ONE
PERPENDICULAR
Forms a 90°angle with a radius
Point of Tangency: The point where the tangent intersects the circle

13. Point of Tangency TOUCHES
Where the tangent line ___________ the circle.
TOUCHES

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

15. Semicircle: An ____ that is ____ of a circle.
arc
half
To name: use 3 letters E D
EDF P F
Measures EXACTLY 180°.

16. ACB AB Major Arc Minor Arc More than 180° Less than 180°P AB
To name: use 3 letters C
To name: use 2 letters B
Part of a circle’s circumference that is ____ than its semicircle.
Part of a circle’s circumference that is ________ than its semicircle.
LESS
GREATER

17. Central Angle : An Angle with its ______ at the _____ of the circle
vertex
center A P C B
APB is a Central Angle

18. measure of an arc = measure of central angle
96 Q
m AB =
96° B C
m ACB =
264°
m AE =
84°
Example 1

19. A semicircle has 180 degrees Vertical Angles are Equal
Always Remember
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
Linear Pairs total 180°.

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

21. Tell me the measure of the following arcs.
m DAB =
240 D A
140
260
m BCA = R
40
100
80 C B
Example 2

22. CONGRUENT ARCS
Two arcs that have the same ______ measurement and are either of the same circle or two congruent circles.
angle C B D 45 45
110 A
Arc length is proportional to “r”