1. Unit 3
Circles

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

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

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

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

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

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

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

9. 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

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

11. 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

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

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

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

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

16. 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

17. 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”

18. Warm up

19. Central Angle
Angle = Arc

20. Inscribed Angle
Angle where the vertex in ON the circle

21. Inscribed Angle

22. 160
The arc is twice as big as the angle!!
80

23. Find the value of x and y.
120  x  y 

24. x = 22 112  Examples 1. If mJK = 80 and JMK = 2x – 4, find x.
2. If mMKS = 56, find m MS.
112  M Q K S J

25. Find the measure of DOG and DIG
72˚ G
If two inscribed angles intercept the same arc, then they are congruent. O I

26. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

27. Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY

28. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.

29. x = 3 In J, m3 = 5x and m 4 = 2x + 9. Example 3
Find the value of x. 3 Q D J T U 4
x = 3

30. Example 4
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
4x – 14 = 90 H K G N
x = 26
Bonus: What type of triangle is this? Why?

31. y = 70 z = 95 110 + y =180 z + 85 = 180 Example 5 Find y and z. z 110

32. 244 x = 105 y = 100 Warm Up 1. Solve for arc ABC
2. Solve for x and y.
x = 105
y = 100

33. Wheel of Formulas!!

34. Vertex is INSIDE the Circle NOT at the Center

35. Ex. 1 Solve for x X
88
84
x = 100

36. Ex. 2 Solve for x.
45
93 xº
89
x = 89

37. Vertex is OUTside the Circle

38. Ex. 3 Solve for x. x
15°
65°
x = 25

39. Ex. 4 Solve for x.
27° x
70°
x = 16

40. Ex. 5 Solve for x.
260° x
x = 80

41. Tune: If You’re Happy and You Know It
If the vertex is ON the circle half the arc. <clap, clap>
If the vertex is INside the circle half the sum. <clap, clap>
But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the difference anyway. <clap, clap>

42. Warm up: Solve for x 1.) 2.) 4.) 3.) 124◦ 70◦ x 18◦ x 260◦ x 20◦ 110◦

43. Circumference & Arc Length of Circles

44. 2 Types of Answers Exact Rounded Type the Pi button on your calculator
Toggle your answer
Round
Exact
Type the Pi button on your calculator
Pi will be in your answer
TI 36X Pro gives exact answers

45. The distance around a circle
Circumference
The distance around a circle

46. Circumference or

47. Find the EXACT circumference.
r = 14 feet
d = 15 miles

48. Ex 3 and 4: Find the circumference. Round to the nearest tenth.
33 yd
14.3 mm

49. 5. A circular flower garden has a radius of 3 feet
5. A circular flower garden has a radius of 3 feet. Find the circumference of the garden to the nearest hundredths.
C = ft

50. Arc Length
The distance along the curved line making the arc (NOT a degree amount)

51. Arc Length

52. Ex 6. Find the Arc Length Round to the nearest hundredths8m 
70

53. Ex 7. Find the exact Arc Length.

54. Ex 8 Find the radius. Round to the nearest hundredth.
60◦ B

55. Ex 9 Find the circumference. Round to the nearest hundredth.
80◦  B

56. Ex 10 Find the radius of the unshaded region
Ex 10 Find the radius of the unshaded region. Round to the nearest tenth. A
75◦ B 