2. Essential Questions
• What are the relationships among parts of
a circle?
• What are the properties of circles and how
do you apply them?
• Where you’ll see this:
• Market research, food service, art,
recreation, navigation
Wed, Feb 02
3. Vocabulary
1. Circle:
2. Radius:
3. Chord:
4. Diameter:
5. Central Angle:
Wed, Feb 02
4. Vocabulary
1. Circle: All points that are the same distance from a
fixed center point; 360° total
2. Radius:
3. Chord:
4. Diameter:
5. Central Angle:
Wed, Feb 02
5. Vocabulary
1. Circle: All points that are the same distance from a
fixed center point; 360° total
2. Radius: A segment whose endpoints are the center
of a circle and on the circle
3. Chord:
4. Diameter:
5. Central Angle:
Wed, Feb 02
6. Vocabulary
1. Circle: All points that are the same distance from a
fixed center point; 360° total
2. Radius: A segment whose endpoints are the center
of a circle and on the circle
3. Chord: A segment where both endpoints are on the
circle
4. Diameter:
5. Central Angle:
Wed, Feb 02
7. Vocabulary
1. Circle: All points that are the same distance from a
fixed center point; 360° total
2. Radius: A segment whose endpoints are the center
of a circle and on the circle
3. Chord: A segment where both endpoints are on the
circle
4. Diameter: A chord that goes through the center of a
circle
5. Central Angle:
Wed, Feb 02
8. Vocabulary
1. Circle: All points that are the same distance from a
fixed center point; 360° total
2. Radius: A segment whose endpoints are the center
of a circle and on the circle
3. Chord: A segment where both endpoints are on the
circle
4. Diameter: A chord that goes through the center of a
circle
5. Central Angle: An angle where the vertex is the
center of the circle
Wed, Feb 02
9. Vocabulary
6. Arc:
7. Semicircle:
8. Minor Arc:
9. Major Arc:
10. Inscribed Angle:
Wed, Feb 02
10. Vocabulary
6. Arc: A section of the circumference of a circle
7. Semicircle:
8. Minor Arc:
9. Major Arc:
10. Inscribed Angle:
Wed, Feb 02
11. Vocabulary
6. Arc: A section of the circumference of a circle
7. Semicircle: An arc that is half of the circumference;
half a circle
8. Minor Arc:
9. Major Arc:
10. Inscribed Angle:
Wed, Feb 02
12. Vocabulary
6. Arc: A section of the circumference of a circle
7. Semicircle: An arc that is half of the circumference;
half a circle
8. Minor Arc: An arc that is less than half the
circumference; same measure as the central angle
9. Major Arc:
10. Inscribed Angle:
Wed, Feb 02
13. Vocabulary
6. Arc: A section of the circumference of a circle
7. Semicircle: An arc that is half of the circumference;
half a circle
8. Minor Arc: An arc that is less than half the
circumference; same measure as the central angle
9. Major Arc: An arc that is more than half the
circumference
10. Inscribed Angle:
Wed, Feb 02
14. Vocabulary
6. Arc: A section of the circumference of a circle
7. Semicircle: An arc that is half of the circumference;
half a circle
8. Minor Arc: An arc that is less than half the
circumference; same measure as the central angle
9. Major Arc: An arc that is more than half the
circumference
10. Inscribed Angle: An angle whose vertex is on the
circle and whose sides are chords of the circle; half
the measure of the arc it contains
Wed, Feb 02
25. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
Wed, Feb 02
26. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132°
Wed, Feb 02
27. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82°
Wed, Feb 02
28. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82°
x°
Wed, Feb 02
29. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82°
x° x°
Wed, Feb 02
30. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
x + x +132 + 82 = 360
132° 82°
x° x°
Wed, Feb 02
31. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
x + x +132 + 82 = 360
132° 82°
2x + 214 = 360
x° x°
Wed, Feb 02
32. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
x + x +132 + 82 = 360
132° 82°
2x + 214 = 360
−214 −214
x° x°
Wed, Feb 02
33. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
x + x +132 + 82 = 360
132° 82°
2x + 214 = 360
−214 −214
2x =146
x° x°
Wed, Feb 02
34. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
x + x +132 + 82 = 360
132° 82°
2x + 214 = 360
−214 −214
2x =146
2 2
x° x°
Wed, Feb 02
35. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
x + x +132 + 82 = 360
132° 82°
2x + 214 = 360
−214 −214
2x =146
2 2
x° x° x = 73
Wed, Feb 02
36. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
x + x +132 + 82 = 360
132° 82°
2x + 214 = 360
−214 −214
2x =146
2 2
73° 73° x = 73
Wed, Feb 02
37. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82°
73° 73°
Wed, Feb 02
38. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠ABC = (mAD + mCD
2
73° 73°
Wed, Feb 02
39. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠ABC = (mAD + mCD
2
1
= (73 + 73)
2
73° 73°
Wed, Feb 02
40. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠ABC = (mAD + mCD
2
1 1
= (73 + 73) = (146)
2 2
73° 73°
Wed, Feb 02
41. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠ABC = (mAD + mCD
2
1 1
= (73 + 73) = (146) = 73°
2 2
73° 73°
Wed, Feb 02
42. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82°
73° 73°
Wed, Feb 02
43. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠BCD = (mAD + mAB
2
73° 73°
Wed, Feb 02
44. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠BCD = (mAD + mAB
2
1
= (73 +132)
2
73° 73°
Wed, Feb 02
45. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠BCD = (mAD + mAB
2
1 1
= (73 +132) = (205)
2 2
73° 73°
Wed, Feb 02
46. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠BCD = (mAD + mAB
2
1 1
= (73 +132) = (205) =102.5°
2 2
73° 73°
Wed, Feb 02
47. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82°
73° 73°
Wed, Feb 02
48. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠CDA = (mBC + mAB
2
73° 73°
Wed, Feb 02
49. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠CDA = (mBC + mAB
2
1
= (82 +132)
2
73° 73°
Wed, Feb 02
50. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠CDA = (mBC + mAB
2
1 1
= (82 +132) = (214)
2 2
73° 73°
Wed, Feb 02
51. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠CDA = (mBC + mAB
2
1 1
= (82 +132) = (214) =107°
2 2
73° 73°
Wed, Feb 02
52. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82°
73° 73°
Wed, Feb 02
53. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠DAB = (mBC + mCD
2
73° 73°
Wed, Feb 02
54. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠DAB = (mBC + mCD
2
1
= (82 + 73)
2
73° 73°
Wed, Feb 02
55. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠DAB = (mBC + mCD
2
1 1
= (82 + 73) = (155)
2 2
73° 73°
Wed, Feb 02
56. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
1 )
132° 82° m∠DAB = (mBC + mCD
2
1 1
= (82 + 73) = (155) = 77.5°
2 2
73° 73°
Wed, Feb 02
57. Example 1
≅ CD . Find the measures of the
In circle O, AD
angles of quadrilateral ABCD, when
=132° and mBC = 82°.
mAB
132° 82° m∠ABC = 73°
m∠BCD =102.5°
m∠CDA =107°
73° 73°
m∠DAB = 77.5°
Wed, Feb 02
58. Example 2
Identify the following for circle P.
a. Diameter b. Radius
c. Chord
d. mLM
e. mLMK f. mLJ
g. m∠LKJ h. Central Angle
Wed, Feb 02
59. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK
c. Chord
d. mLM
e. mLMK f. mLJ
g. m∠LKJ h. Central Angle
Wed, Feb 02
60. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
e. mLMK f. mLJ
g. m∠LKJ h. Central Angle
Wed, Feb 02
61. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL
e. mLMK f. mLJ
g. m∠LKJ h. Central Angle
Wed, Feb 02
62. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47°
e. mLMK f. mLJ
g. m∠LKJ h. Central Angle
Wed, Feb 02
63. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47° =109°
e. mLMK f. mLJ
g. m∠LKJ h. Central Angle
Wed, Feb 02
64. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47° =109°
e. mLMK f. mLJ
= 62° +180°
g. m∠LKJ h. Central Angle
Wed, Feb 02
65. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47° =109°
e. mLMK f. mLJ
= 62° +180° = 242°
g. m∠LKJ h. Central Angle
Wed, Feb 02
66. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47° =109°
e. mLMK f. mLJ
= 62° +180° = 242° = 62°
g. m∠LKJ h. Central Angle
Wed, Feb 02
67. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47° =109°
e. mLMK f. mLJ
= 62° +180° = 242° = 62°
g. m∠LKJ h. Central Angle
= 2 (62°)
1
Wed, Feb 02
68. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47° =109°
e. mLMK f. mLJ
= 62° +180° = 242° = 62°
g. m∠LKJ h. Central Angle
= 2 (62°) = 31°
1
Wed, Feb 02
69. Example 2
Identify the following for circle P.
a. Diameter b. Radius
JK KP
c. Chord
d. mLM
KL = 62° + 47° =109°
e. mLMK f. mLJ
= 62° +180° = 242° = 62°
g. m∠LKJ h. Central Angle
= 2 (62°) = 31°
1
∠JPM
Wed, Feb 02
71. Problem Set
p. 228 #1-25 odd
“We are so accustomed to disguise ourselves to others
that in the end we become disguised to ourselves.”
- Francois de La Rochefoucauld
Wed, Feb 02
