This document provides definitions and examples related to circles. It begins by defining key circle vocabulary terms like radius, diameter, chord, circumference, and pi. Examples are then provided to demonstrate finding parts of circles, calculating circumference, and solving problems involving radii, diameters and arc lengths. The final example finds the exact circumference of a circle given the length of its diameter. Overall, the document introduces fundamental concepts of circles and provides practice applying definitions and formulas to solve circle measurement problems.

1. CHAPTER 10
CIRCLES
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2. SECTION 10-1
Circles and Circumference
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3. ESSENTIAL QUESTIONS
How do you identify and use parts of circles?
How do you solve problems involving the
circumference of a circle?
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4. VOCABULARY
1. Circle:
2. Center:
3. Radius:
4. Chord:
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5. VOCABULARY
1. Circle: The set of points that are all the same
distance from a given point
2. Center:
3. Radius:
4. Chord:
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6. VOCABULARY
1. Circle: The set of points that are all the same
distance from a given point
2. Center: The point that all of the points of a circle
are equidistant from
3. Radius:
4. Chord:
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7. VOCABULARY
1. Circle: The set of points that are all the same
distance from a given point
2. Center: The point that all of the points of a circle
are equidistant from
3. Radius: A segment with one endpoint at the center
and the other on the edge of the circle; also the
distance from the center to the edge of the circle
4. Chord:
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8. VOCABULARY
1. Circle: The set of points that are all the same
distance from a given point
2. Center: The point that all of the points of a circle
are equidistant from
3. Radius: A segment with one endpoint at the center
and the other on the edge of the circle; also the
distance from the center to the edge of the circle
4. Chord: A segment with both endpoints on the
edge of the circle
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9. VOCABULARY
5. Diameter:
6. Congruent Circles:
7. Concentric Circles:
8. Circumference:
9. Pi (π):
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10. VOCABULARY
5. Diameter: A special chord that passes through the
center of a circle; twice the length of the radius
6. Congruent Circles:
7. Concentric Circles:
8. Circumference:
9. Pi (π):
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11. VOCABULARY
5. Diameter: A special chord that passes through the
center of a circle; twice the length of the radius
6. Congruent Circles: Two or more circles with
congruent radii
7. Concentric Circles:
8. Circumference:
9. Pi (π):
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12. VOCABULARY
5. Diameter: A special chord that passes through the
center of a circle; twice the length of the radius
6. Congruent Circles: Two or more circles with
congruent radii
7. Concentric Circles: Coplanar circles with the same
center
8. Circumference:
9. Pi (π):
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13. VOCABULARY
5. Diameter: A special chord that passes through the
center of a circle; twice the length of the radius
6. Congruent Circles: Two or more circles with
congruent radii
7. Concentric Circles: Coplanar circles with the same
center
8. Circumference: The distance around a circle
9. Pi (π):
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14. VOCABULARY
5. Diameter: A special chord that passes through the
center of a circle; twice the length of the radius
6. Congruent Circles: Two or more circles with
congruent radii
7. Concentric Circles: Coplanar circles with the same
center
8. Circumference: The distance around a circle
9. Pi (π): The irrational number found from the ratio
of circumference to the diameter
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15. VOCABULARY
10. Inscribed:
11. Circumscribed:
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16. VOCABULARY
10. Inscribed: A polygon inside a circle where all of
the vertices of the polygon are on the circle
11. Circumscribed:
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17. VOCABULARY
10. Inscribed: A polygon inside a circle where all of
the vertices of the polygon are on the circle
11. Circumscribed: A circle that is around a polygon
that is inscribed
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18. EXAMPLE 1
a. Name the circle
b. Identify a radius
c. Identify a chord d. Name the diameter
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19. EXAMPLE 1
a. Name the circle
Circle C or ⊙C
b. Identify a radius
c. Identify a chord d. Name the diameter
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20. EXAMPLE 1
a. Name the circle
Circle C or ⊙C
b. Identify a radius
AC or CD
c. Identify a chord d. Name the diameter
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21. EXAMPLE 1
a. Name the circle
Circle C or ⊙C
b. Identify a radius
AC or CD
c. Identify a chord d. Name the diameter
EB
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22. EXAMPLE 1
a. Name the circle
Circle C or ⊙C
b. Identify a radius
AC or CD
c. Identify a chord d. Name the diameter
EB AD
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23. EXAMPLE 2
If JT = 24 in, what is KM?
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24. EXAMPLE 2
If JT = 24 in, what is KM?
JT = KL
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25. EXAMPLE 2
If JT = 24 in, what is KM?
JT = KL
KL = 24 in
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26. EXAMPLE 2
If JT = 24 in, what is KM?
JT = KL
KL = 24 in
KM is half of KL
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27. EXAMPLE 2
If JT = 24 in, what is KM?
JT = KL
KL = 24 in
KM is half of KL
KM = 12 in
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28. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
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29. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
22
LN =
2
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30. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
22
LN = =11
2
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31. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
22 16
LN = =11 MP =
2 2
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32. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
22 16
LN = =11 MP = = 8
2 2
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33. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
22 16
LN = =11 MP = = 8
2 2
LP = LN + MP − MN
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34. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
22 16
LN = =11 MP = = 8
2 2
LP = LN + MP − MN
LP =11+ 8 − 5
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35. EXAMPLE 3
The diameter of ⊙L is 22 cm and the diameter of
⊙P is 16 cm. MN = 5 cm. Find LP.
22 16
LN = =11 MP = = 8
2 2
LP = LN + MP − MN
LP =11+ 8 − 5
LP =14 cm
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36. EXAMPLE 4
Find the diameter and radius of a circle to the nearest
hundredth if the circumference of the circle is 65.4 feet.
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37. EXAMPLE 4
Find the diameter and radius of a circle to the nearest
hundredth if the circumference of the circle is 65.4 feet.
C = πd
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38. EXAMPLE 4
Find the diameter and radius of a circle to the nearest
hundredth if the circumference of the circle is 65.4 feet.
C = πd
65.4 = π d
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39. EXAMPLE 4
Find the diameter and radius of a circle to the nearest
hundredth if the circumference of the circle is 65.4 feet.
C = πd
65.4 = π d
π π
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40. EXAMPLE 4
Find the diameter and radius of a circle to the nearest
hundredth if the circumference of the circle is 65.4 feet.
C = πd
65.4 = π d
π π
d ≈ 20.82 ft
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41. EXAMPLE 4
Find the diameter and radius of a circle to the nearest
hundredth if the circumference of the circle is 65.4 feet.
C = πd
65.4 = π d
π π
d ≈ 20.82 ft
r ≈10.41 ft
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42. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
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43. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
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44. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r + r = (3 2 )
2 2 2
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45. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r + r = (3 2 )
2 2 2
2r = (3 2 )
2 2
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46. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r + r = (3 2 )
2 2 2
2r = (3 2 )
2 2
2r = 9(2)
2
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47. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r + r = (3 2 )
2 2 2
2r = (3 2 )
2 2
2r = 9(2)
2
r =9
2
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48. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r = 9
2
r + r = (3 2 )
2 2 2
2r = (3 2 )
2 2
2r = 9(2)
2
r =9
2
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49. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r = 9
2
r + r = (3 2 )
2 2 2
r =3
2r = (3 2 )
2 2
2r = 9(2)
2
r =9
2
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50. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r = 9
2
r + r = (3 2 )
2 2 2
r =3
2r = (3 2 )
2 2
C = 2π r
2r = 9(2)
2
r =9
2
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51. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r = 9
2
r + r = (3 2 )
2 2 2
r =3
2r = (3 2 )
2 2
C = 2π r
2r = 9(2)
2
C = 2π (3)
r =9
2
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52. EXAMPLE 5
Find the exact circumference of ⊙R.
BF = 3 2
(BR) + (RF ) = (BF )
2 2 2
r = 9
2
r + r = (3 2 )
2 2 2
r =3
2r = (3 2 )
2 2
C = 2π r
2r = 9(2)
2
C = 2π (3)
r =9
2
C = 6π
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53. CHECK YOUR
UNDERSTANDING
p. 687 #1-9
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54. PROBLEM SET
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55. PROBLEM SET
p. 687 #11-41 odd, 71
“We don't know who we are until we see what
we can do.” - Martha Grimes
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