CirclesParts of a CircleClass WorkUse the diagram of the circle with center A to answer the following:

1. Name the radii2. Name the chord(s)3. Name the diameter(s)4. If AC= 7, what does TC=?5. If CT= 13, what does MA=?6. Draw a tangent line to the circle at M.7. What is the difference between a chord and a secant?

Draw the common tangents for each set of circles.8. 9. 10.

11. If a circle has a center of (7,6) and is tangent to the x-axis, how big is the radius?12. If a circle has a center of (7,6) and is tangent to the y-axis, how big is the diameter?

HomeworkUse the diagram of the circle with center C to answer the following:

13. Name the radii14. Name the chord(s)15. Name the diameter(s)16. If CE=8, what does BD=?17. Which is longer DB or AB? Justify.18. Draw a tangent line to the circle at A.19. What is the difference between a tangent and a secant?

Draw the common tangents for each set of circles.20. 21. 22.

23. If a circle has a center of (3,-6) and is tangent to the x-axis, how long is the radius?24. If a circle has a center of (3, -6) and is tangent to the y-axis, how long is the diameter?

Angles & ArcsClass WorkIn C, m∠BCD=110 ,m∠ ACE=80, and CE= 5, find the following

25. m AE26. m AB

Geometry - Circles ~1~ NJCTL.org

27. m AD28. mEBD29. mBED30. lengthof AE31. lengthof m AB32. lengthof AD33. lengthof EBD34. lengthof BED

35. If the central angle of a circle has measure 60o and makes a minor arc with length 15, what is the radius?

36. If the arc of a circle has length 8π and the circumference of the circle is 24π, what is the measure of the central angle that intercepts the arc?

Two concentric circles have center P, PS=6 and SU=4.37. Which is greater: m RS∨mTU ?38. Which is greater: the length of RS∨the lengthof TU ?39. ∠TPU=90 °, how long would chord TU be?

HomeworkIn C, m∠BCD=130 ,m∠ ACE=60, and CE= 8, find the following

40. m AE41. m AB42. m AD43. mEBD44. mBED45. lengthof AE46. lengthof m AB47. lengthof AD48. lengthof EBD49. lengthof BED

50. If the central angle of a circle has measure 80o and makes a minor arc with length 12, what is the radius?

51. If the arc of a circle has length 10π and the circumference of the circle is 30π, what is the measure of the central angle that intercepts the arc?

Two concentric circles have center P, PS=3 and SU=3.52. Which is greater: m RS∨mTU ?53. Which is greater: the length of RS∨the lengthof TU ?

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54. ∠TPU=90 °, how long would chord TU be?

Chords, Inscribed Angles, & PolygonsClass WorkSolve for the variable in each problem. C is the center of the circle.55. 56. 57.

58. 59. 60.

61. 62. 63.

64. 65. 66.

67. 68. 69.

70. 71. 72.

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HomeworkSolve for the variable in each problem. C is the center of the circle.73. 74. 75.

76. 77. 78.

79. 80. 81.

82. 83. 84.

85. 86. 87.

88. 89. 90.

Tangents & SecantsClass WorkSolve for the variable in each problem. C is the center of the circle.91. 92. 93.

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94. 95. 96.

97. 98. 99.

100. 101. 102.

103. 104. 105.

106. 107. 108.

HomeworkSolve for the variable in each problem. C is the center of the circle.109. 110. 111.

112. 113. 114.

115. 116. 117.

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118. 119. 120.

121. 122. 123.

124. 125. 126.

Segments & CirclesClass WorkFind the value of the variable. C is the center of the circle.127. 128. 129.

130. 131. 132.

133. 134. 135.

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HomeworkFind the value of the variable. C is the center of the circle.136. 137. 138.

139. 140. 141.

142. 143. 144.

Equations of a CircleClass WorkWhat are the center and the radius of the following circles?

145. ( x+2 )2+ ( y−4 )2=16146. ( x−3 )2+( y−7 )2=25147. ( x )2+ ( y+8 )2=1148. ( x−7 )2+( y+1 )2=17149. ( x+6 )2+( y )2=32

Write the standard form of the equation for the given information.150. center (3,2) radius 6151. center (-4, -7) radius 8152. center (5, -9) radius 10153. center (-8, 0) diameter 14154. center (4,5) and point on the circle (3, -7)155. diameter with endpoints (6, 4) and (10, -8)156. center (4, 9) and tangent to the x-axis157. x2+4 x+ y2−8 y=11158. x2−10 x+ y2+2 y=11

Geometry - Circles ~7~ NJCTL.org

d=15 in

95or=10 cm100o

R=6ft.220o

450R=3in

R=6ft.220o

r=10 cm100o

d=15 in

95o450R=3in

159. x2+7x+ y2=11Are the following points on the circle (x-3)2+(y+4)2=25? Support your answer with your work.

160. (3,1)161. (0,0)162. (4,-1)

HomeworkWhat are the center and the radius of the following circles?

163. ( x−9 )2+ ( y+5 )2=9164. ( x+11)2+( y−8 )2=64165. ( x+13 )2+( y−3 )2=144166. ( x−2 )2+( y )2=19167. ( x−6 )2+ ( y−15 )2=40

Write the standard form of the equation for the given information.168. center (-2, -4) radius 9169. center (-3, 3) radius 11170. center (5, 8) radius 12171. center (0 , 8) diameter 16172. center (-4,6) and point on the circle (-2, -8)173. diameter with endpoints (5, 14) and (11, -8)174. center (4, 9) and tangent to the y-axis175. x2−2 x+ y2+10 y=11176. x2+12x+ y2+20 y=11177. 4 x2+16 x+4 y2−8 y=12

Are the following points on the circle (x-5)2+(y-12)2=169? Support your answer with your work.178. (-4,2)179. (0,0)180. (-7,7)

Area of a SectorClassworkFind the area of the minor sector. Round to the nearest hundredth or leave your answer in terms of pi.181. 182. 183. 184.

Find the area of the major sector. Round to the nearest hundredth or leave your answer in terms of pi.185. 186. 187. 188.

Geometry - Circles ~8~ NJCTL.org

47o

d=21inr=2.3 cm

74o105o

r=6.7 md=10ft.

115o

r=2.3 cm74o

105o

r=6.7 md=10ft.

115o

47o

d=21in

HomeworkFind the area of the minor sector. Round to the nearest hundredth or leave your answer in terms of pi.189. 190. 191. 192.

Find the area of the major sector. Round to the nearest hundredth or leave your answer in terms of pi.193. 194. 195. 196.

Multiple ChoiceFor questions 1-3, use the diagram at the right of F

1. Name a secant of the circlea. FA b. AC c. BE d. BC

2. BF= 7 and tangent BE= 9, what is AE?a. 5.656 b. 11.402 c. 4.402 d.2.402

3. m∠BCA=20 and BD= 8, what is the length of BC?a. 1.396 b. 2.793 c. 9.774 d. 19.548

4. If AB is a diameter and m AC=50 °, then what is the measure of ABC?a. 50 ° b. 130 ° c. 230 ° d. 310 °

5. What is the area of the major sector for the circle in question 4.

6. Find a .a. 200b. 300c. 240d. 20

7. Find b.

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a. 70b. 110c. 150d. 210

8. Find c.a. 65b. 35c. 30d. not enough information

9. Find d.a. 20b. 40c. 50d. 70

10. Find e.a. 7.5b. 8c. 8.5d. 9

11. Find f.a. 2b. 3c. 4d. 6

12. Find g.a. 2b. 5.3c. 8d. 10

13. Find x.a. 3b. 6.75c. 9d. 15

14. What is the equation of the circle drawn?a. ( x−4 )2+( y−6 )2=4b. ( x+4 )2+ ( y+6 )2=6c. ( x−4 )2+( y−6 )2=16d. ( x+4 )2+ ( y+6 )2=36

Geometry - Circles ~10~ NJCTL.org

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Extended Response1. The points (3,2) and (9,12) are the endpoints of a diameter of a circle

a. Where is the center of the circle?b. How long is the diameter of the circle?c. Write the equation of the circle?d. Is the point (5,6) on the circle? Justify your answer.

2. S, T, U, and V are points of tangency of A and B. TH= 4x+8, SH= 6x+4, HU=x+2y, and HV= 4x-2y.

a. Find x. b. Find y.c. If AB= 25 and UB(not drawn)=5, what is the

length of AT(not drawn)?

3. In the diagram AB∥CD and CD is a diameter.a. If m AB=40 find the measure of BC .b. If AB= 12 and CD= 20, how far the center is AB?c. Using the information from parts a and b, how long is ACB?

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Answer Key1. Segments AT, AM, AC2. Segments JH, TC3. Segment TC4. 145. 6.56. Tangent line touches the circle at M7. A chord has endpoints on the circle,

while a secant passes through.8. Four tangent lines. Two of the tangent

lines touch the outsides of the two circles, while the other two make a diagonal in the middle of the two circles.

9. Two tangent lines on the outsides of the two circles.

10. One tangent line at the bottom11. R=612. D=1413. Segments CD, CB, and CE14. Segments AB, DB15. Segment DB16. 1617. Segment DB, diameter is longest

chord of a circle18. Tangent line passes through A19. A tangent “touches” at one point, while

a secant touches at two points20. Two tangent lines on the outside. Two

more tangent lines making a diagonal through the middle.

21. One tangent line through the center of the two touching circles. Two more tangent lines, one at the top and one at the bottom.

22. No tangent lines23. R=624. R=625. 8026. 7027. 18028. 26029. 25030. 6.98

31. 6.1032. 15.733. 22.6934. 21.8235. 45/π36. 120 degrees37. They are equal38. TU is longer39. 10√240. 6041. 5042. 18043. 24044. 23045. 8.3846. 6.9847. 25.1348. 33.5149. 32.1150. 8.5951. 120 degrees52. They are equal53. TU is longer54. 6√255. X=456. 42 degrees57. 30 degrees58. X=359. X=860. 50 degrees61. X=562. 84 degrees63. X=14564. 20 degrees65. 140 degrees66. 90 degrees67. X=170 degrees68. X=20 degrees69. X=9570. X=70 degrees71. a=25; b=2072. x=80 degrees73. v=4

Geometry - Circles ~13~ NJCTL.org

74. b= 80 degrees75. n=220 degrees76. F=40 degrees77. R=9.8578. x=479. x=880. 5081. k=14082. d=8083. h=60 degrees84. g=5.6685. d=8086. e=3587. n=6088. d=110 degrees89. e=5 f=3090. f=11091. x=1292. x=993. x=494. c=4195. g=896. x=2, y=697. c=1098. x=799. x=8100. a=35101. k=40102. x=130103. h=220104. f=80105. g=60106. 65107. b=130108. m=120109. f=9110. t=25111. 2.49112. g=7113. g=10114. x=3; y=2115. j=12116. r=11117. x=7

118. d=80119. x=70/3120. x=220121. 40 degrees122. 140 degrees123. x=210124. a=30 degrees125. d=135126. d=60 degrees127. n=6.4128. x=8129. x=4130. x=2131. x=3132. x=5.48133. x=6134. x=9135. x=4136. n=4137. r=5138. h=2139. x=8140. y=1141. k=3.37142. v=4.47143. x=2.25144. a=1.66145. C(-2,4); r=4146. C (3,7); r=5147. C (),-8); r=1148. C (7,-1); r= √17149. C (-6,0); r =4√2150. (x-3)2 + (x-2)2 =36151. (x+4)2 + (Y+7)2 =64152. (x-5)2 + (y+9)2 = 100153. (x+8)2 + y2 =49154. (x-4)2 + (y-5)2 =145155. (x-8)2 + (y+2)2 =40156. (x-4)2 + (y-9)2 =81157. (x+2)2 + (y-4)2 =31158. (x-5)2 + (y+1)2 =37159. (x+3.5)2 + y2 =23.25160. yes; (3-3)2+(1+4)2=25161. yes; (0-3)2+(0+4)2=25

Geometry - Circles ~14~ NJCTL.org

162. no; (4-3)2+(-1+4)2=10163. C (9,-5) r=3164. C -11, 8) r=8165. C(-13, 3) r=12166. C(2,0) r= √19167. C (6,15) r=2√10168. (x+2)2 +(Y+4)2 =81169. (x+3)2 + (y-3)2 =121170. (x-5)2 + (y-8)2 =144171. X2 + (y-8)2 =64172. (x+4)2 + (y-6)2 =200173. (x-8)2 + (y-3)2 = 130174. (x-4)2 + ( y-9)2 =130175. (x-1)2 + (y+5)2 =37176. (x+6)2 + (y+10)2 =147177. (x+2)2 + (y-1)2 =8178. no; (-4-5)2+(2-12)2=181179. yes; (0-5)2+(0-12)2=169180. yes; (-7-5)2+(7-12)2=169181. A = 1.125π in2/3.53 in2

182. A=14π / 43.98 ft2

183. A=27.78π / 87.27 cm2

184. A=53.13π / 166.9 in2

185. A=7.77π / 24.4 in2

186. A=22π / 69.12 ft2

187. A=72.22π / 226.89 cm2

188. A=112.5π / 353.43 in2

189. A=18.06π / 56.72 ft2

190. A=13.09π / 41.13 m2

191. A=1.09π / 3.42 cm2

192. A=57.58π / 180.88 in2

193. A=50π / 157.08 ft2

194. A=31.8π / 99.89 m2

195. A=4.2π / 13.2 cm2

196. A=220.5π / 692.72 in2

Multiple Choice1. C2. C3. C4. D5. A6. C7. C

8. A9. D10. C11. A12. A13. C

Extended Response1. a) (6,7) (b) 11.662

(c) ( x−6 )2+( y−7 )2=136

(d) no; (5−6 )2+ (6−7 )2=2 2. (a) 2 (b) 1.5 (c) 33. (a) 110 (b) 8 (c) 55.851

Geometry - Circles ~15~ NJCTL.org