1. Circles
Chapter 10.1

2. Identify and use parts of circles.
Solve problems involving the circumference of a circle.
circle
diameter
circumference
pi ()
center
chord
radius
Standard 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. (Key)
Lesson 1 MI/Vocab

3. Circle Terms
Def: The set of all points a given distance from a given point.
The given point is the Center
The given distance is the Radius
A circle with center P is called “circle P” or P

4. Circle Distances
The distance from the center to any point on the circle is called the radius
All radii of a circle are congruent
All circles with equal radii are congruent
The distance across the circle, through its center, is the diameter of the circle
The diameter is twice the radius
The distance around the circle is called the circumference. C = 2πr or C = πd

5. Find Radius and Diameter
Formula for radius
Substitute and simplify.
Answer: 9
Lesson 1 Ex2

6. Find Radius and Diameter
Since all radii are congruent, RN = RP.
Answer: So, RP = 2.
Lesson 1 Ex2

7. A. 6.25
B. 12.5
C. 25
D. 50 A B C D
Lesson 1 CYP2

8. A. 7.25
B. 14.5
C. 29
D. 58 A B C D
Lesson 1 CYP2

9. A. 4.25
B. 8.5
C. 17
D. 85 A B C D
Lesson 1 CYP2

10. Find Measures in Intersecting Circles10 22 5
= 27
Lesson 1 Ex3

11. A. 2.5 in.
B. 4.5 in.
C. 6.5 in.
D. 9 in. A B C D
Lesson 1 CYP3

12. A in.
B in.
C. 13 in.
D in. A B C D
Lesson 1 CYP3

13. It takes just over three diameters to wrap around a circle.

14. π and Circumference Circumference: The distance around a circle
C = 2πr or C = πd
Pi  π = irrational number
In this class, leave all answers in terms of π
Ex: 5π or

15. A. Find C if r = 13 inches. Answer: 26 or ≈ 81.68 in.
Find Circumference, Diameter, and Radius
A. Find C if r = 13 inches.
Circumference formula
Substitution
Answer: 26 or ≈ in.
Lesson 1 Ex4

16. B. Find C if d = 6 millimeters.
Find Circumference, Diameter, and Radius
B. Find C if d = 6 millimeters.
Circumference formula
Substitution
Answer: 6 or ≈ mm
Lesson 1 Ex4

17. C. Find d and r to the nearest hundredth if C = 65.4 feet.
Find Circumference, Diameter, and Radius
C. Find d and r to the nearest hundredth if C = 65.4 feet.
Circumference formula
Substitution
Divide each side by .
Use a calculator.
Lesson 1 Ex4

18. A. 44 cm.
B cm
C. 22 cm
D cm A B C D
Lesson 1 CYP4

19. A. 1.5 ft
B. 3 ft
C ft
D ft A B C D
Lesson 1 CYP4

20. A. 8.4 m
B m
C m
D m A B C D
Lesson 1 CYP4

21. Segments and Lines
Radius—a segment from the center to any point on the circle
Chord—a segment whose endpoints are on the circle
Diameter—a chord that passes through the center of the circle
Secant—a line that intersects a circle in two points
Tangent—a line that intersects the circle in only one point

22. Secant
Tangent
Diameter
Radius
Point of Tangency
Chord

23. Identify Parts of a Circle
A. Name the circle.
Lesson 1 Ex1

24. Identify Parts of a Circle
B. Name a radius of the circle.
Lesson 1 Ex1

25. Identify Parts of a Circle
C. Name a chord of the circle.
Lesson 1 Ex1

26. Identify Parts of a Circle
D. Name a diameter of the circle.
Lesson 1 Ex1

27. A. Name the circle. A. B. C. D. A B C D
Lesson 1 CYP1

28. B. Name a radius of the circle.
Lesson 1 CYP1

29. C. Name a chord of the circle.B. C. D. A B C D
Lesson 1 CYP1

30. D. Name a diameter of the circle.B. C. D. A B C D
Lesson 1 CYP1

31. Concentric Circles
Circles with the same Center but different radii

32. Special Right Triangle!!!
Use Other Figures to Find Circumference x
Special Right Triangle!!!
45o- 45o-90o
x = 3 = radius
C = 2π(3) = 6π
Lesson 1 Ex5

33. A. B. C. D. A B C D
Lesson 1 CYP5

34. Homework (get it?) Chapter 10-1 Pg 557 # 13 – 52 all, & 60
Yes, it is a lot of problems
but they are very quick.