Circles Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: 1. Name the radii 2. 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? Homework Use the diagram of the circle with center C to answer the following: 13. Name the radii 14. 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 & Arcs Class Work In C, m BCD = 110, m ACE = 80, and CE= 5, find the following 25. mae 26. mab Geometry - Circles ~1~ NJCTL.org
27. mad 28. mebd 29. mbed 30. length of AE 31. length of mab 32. length of AD 33. length of EBD 34. length of BED 35. If the central angle of a circle has measure 60 o 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: mrs or mtu? 38. Which is greater: the length of RS or the length of TU? 39. TPU = 90, how long would chord TU be? Homework In C, m BCD = 130, m ACE = 60, and CE= 8, find the following 40. mae 41. mab 42. mad 43. mebd 44. mbed 45. length of AE 46. length of mab 47. length of AD 48. length of EBD 49. length of BED 50. If the central angle of a circle has measure 80 o 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: mrs or mtu? 53. Which is greater: the length of RS or the length of TU? 54. TPU = 90, how long would chord TU be? Geometry - Circles ~2~ NJCTL.org
Chords, Inscribed Angles, & Polygons Class Work Solve 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. Geometry - Circles ~3~ NJCTL.org
Homework Solve 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 & Secants Class Work Solve for the variable in each problem. C is the center of the circle. 91. 92. 93. Geometry - Circles ~4~ NJCTL.org
94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. Homework Solve for the variable in each problem. C is the center of the circle. 109. 110. 111. 112. 113. 114. 115. 116. 117. Geometry - Circles ~5~ NJCTL.org
118. 119. 120. 121. 122. 123. 124. 125. 126. Segments & Circles Class Work Find the value of the variable. C is the center of the circle. 127. 128. 129. 130. 131. 132. 133. 134. 135. Geometry - Circles ~6~ NJCTL.org
Homework Find the value of the variable. C is the center of the circle. 136. 137. 138. 139. 140. 141. 142. 143. 144. Equations of a Circle Class Work What are the center and the radius of the following circles? 145. (x + 2) 2 + (y 4) 2 = 16 146. (x 3) 2 + (y 7) 2 = 25 147. (x) 2 + (y + 8) 2 = 1 148. (x 7) 2 + (y + 1) 2 = 17 149. (x + 6) 2 + (y) 2 = 32 Write the standard form of the equation for the given information. 150. center (3,2) radius 6 151. center (-4, -7) radius 8 152. center (5, -9) radius 10 153. center (-8, 0) diameter 14 154. 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-axis 157. x 2 + 4x + y 2 8y = 11 158. x 2 10x + y 2 + 2y = 11 159. x 2 + 7x + y 2 = 11 Are the following points on the circle (x-3) 2 +(y+4) 2 =25? Support your answer with your work. 160. (3,1) Geometry - Circles ~7~ NJCTL.org
161. (0,0) 162. (4,-1) Homework What are the center and the radius of the following circles? 163. (x 9) 2 + (y + 5) 2 = 9 164. (x + 11) 2 + (y 8) 2 = 64 165. (x + 13) 2 + (y 3) 2 = 144 166. (x 2) 2 + (y) 2 = 19 167. (x 6) 2 + (y 15) 2 = 40 Write the standard form of the equation for the given information. 168. center (-2, -4) radius 9 169. center (-3, 3) radius 11 170. center (5, 8) radius 12 171. center (0, 8) diameter 16 172. 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-axis 175. x 2 2x + y 2 + 10y = 11 176. x 2 + 12x + y 2 + 20y = 11 177. 4x 2 + 16x + 4y 2 8y = 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 Sector Classwork Find the area of the minor sector. Round to the nearest hundredth or leave your answer in terms of pi. 181. 182. 220 o 183. r=10 cm 184. 45 0 R=3in R=6ft. 100 o 95 o d=15 in Find the area of the major sector. Round to the nearest hundredth or leave your answer in terms of pi. 185. 186. 187. 188. 45 0 R=3in 220 o R=6ft. 100 o r=10 cm 95 o d=15 in Geometry - Circles ~8~ NJCTL.org
Homework Find the area of the minor sector. Round to the nearest hundredth or leave your answer in terms of pi. 189. 190. 191. 192. d=10ft. 115 o 105 o r=6.7 m 74 o 47o r=2.3 cm d=21in Find the area of the major sector. Round to the nearest hundredth or leave your answer in terms of pi. 193. 194. 195. 196. d=10ft. 115 o 105 o r=6.7 m 74 o 47o r=2.3 cm d=21in Multiple Choice For questions 1-3, use the diagram at the right of F 1. Name a secant of the circle a. 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 mac = 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. 200 b. 300 c. 240 d. 20 7. Find b. a. 70 b. 110 c. 150 d. 210 Geometry - Circles ~9~ NJCTL.org
8. Find c. a. 65 b. 35 c. 30 d. not enough information 9. Find d. a. 20 b. 40 c. 50 d. 70 10. Find e. a. 7.5 b. 8 c. 8.5 d. 9 11. Find f. a. 2 b. 3 c. 4 d. 6 12. Find g. a. 2 b. 5. 3 c. 8 d. 10 13. Find x. a. 3 b. 6.75 c. 9 d. 15 14. What is the equation of the circle drawn? a. (x 4) 2 + (y 6) 2 = 4 b. (x + 4) 2 + (y + 6) 2 = 6 c. (x 4) 2 + (y 6) 2 = 16 d. (x + 4) 2 + (y + 6) 2 = 36 Geometry - Circles ~10~ NJCTL.org
Extended Response 1. 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 mab = 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? Geometry - Circles ~11~ NJCTL.org
1. Segments AT, AM, AC 2. Segments JH, TC 3. Segment TC 4. 14 5. 6.5 6. Tangent line touches the circle at M 7. 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 bottom 11. R=6 12. D=14 13. Segments CD, CB, and CE 14. Segments AB, DB 15. Segment DB 16. 16 17. Segment DB, diameter is longest chord of a circle 18. Tangent line passes through A 19. A tangent touches at one point, while a secant touches at two points 20. 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 lines 23. R=6 24. R=6 25. 80 26. 70 27. 180 28. 260 29. 250 30. 6.98 Answer Key 31. 6.10 32. 15.7 33. 22.69 34. 21.82 35. 45/π 36. 120 degrees 37. They are equal 38. TU is longer 39. 10 2 40. 60 41. 50 42. 180 43. 240 44. 230 45. 8.38 46. 6.98 47. 25.13 48. 33.51 49. 32.11 50. 8.59 51. 120 degrees 52. They are equal 53. TU is longer 54. 6 2 55. X=4 56. 42 degrees 57. 30 degrees 58. X=3 59. X=8 60. 50 degrees 61. X=5 62. 84 degrees 63. X=145 64. 20 degrees 65. 140 degrees 66. 90 degrees 67. X=170 degrees 68. X=20 degrees 69. X=95 70. X=70 degrees 71. a=25; b=20 72. x=80 degrees 73. v=4 Geometry - Circles ~12~ NJCTL.org
74. b= 80 degrees 75. n=220 degrees 76. F=40 degrees 77. R=9.85 78. x=4 79. x=8 80. 50 81. k=140 82. d=80 83. h=60 degrees 84. g=5.66 85. d=80 86. e=35 87. n=60 88. d=110 degrees 89. e=5 f=30 90. f=110 91. x=12 92. x=9 93. x=4 94. c=41 95. g=8 96. x=2, y=6 97. c=10 98. x=7 99. x=8 100. a=35 101. k=40 102. x=130 103. h=220 104. f=80 105. g=60 106. 65 107. b=130 108. m=120 109. f=9 110. t=25 111. 2.49 112. g=7 113. g=10 114. x=3; y=2 115. j=12 116. r=11 117. x=7 118. d=80 119. x=70/3 120. x=220 121. 40 degrees 122. 140 degrees 123. x=210 124. a=30 degrees 125. d=135 126. d=60 degrees 127. n=6.4 128. x=8 129. x=4 130. x=2 131. x=3 132. x=5.48 133. x=6 134. x=9 135. x=4 136. n=4 137. r=5 138. h=2 139. x=8 140. y=1 141. k=3.37 142. v=4.47 143. x=2.25 144. a=1.66 145. C(-2,4); r=4 146. C (3,7); r=5 147. C (),-8); r=1 148. C (7,-1); r= 17 149. C (-6,0); r =4 2 150. (x-3) 2 + (x-2) 2 =36 151. (x+4) 2 + (Y+7) 2 =64 152. (x-5) 2 + (y+9) 2 = 100 153. (x+8) 2 + y 2 =49 154. (x-4) 2 + (y-5) 2 =145 155. (x-8) 2 + (y+2) 2 =40 156. (x-4) 2 + (y-9) 2 =81 157. (x+2) 2 + (y-4) 2 =31 158. (x-5) 2 + (y+1) 2 =37 159. (x+3.5) 2 + y 2 =23.25 160. yes; (3-3) 2 +(1+4) 2 =25 161. yes; (0-3) 2 +(0+4) 2 =25 Geometry - Circles ~13~ NJCTL.org
162. no; (4-3) 2 +(-1+4) 2 =10 163. C (9,-5) r=3 164. C -11, 8) r=8 165. C(-13, 3) r=12 166. C(2,0) r= 19 167. C (6,15) r=2 10 168. (x+2) 2 +(Y+4) 2 =81 169. (x+3) 2 + (y-3) 2 =121 170. (x-5) 2 + (y-8) 2 =144 171. X 2 + (y-8) 2 =64 172. (x+4) 2 + (y-6) 2 =200 173. (x-8) 2 + (y-3) 2 = 130 174. (x-4) 2 + ( y-9) 2 =130 175. (x-1) 2 + (y+5) 2 =37 176. (x+6) 2 + (y+10) 2 =147 177. (x+2) 2 + (y-1) 2 =8 178. no; (-4-5) 2 +(2-12) 2 =181 179. yes; (0-5) 2 +(0-12) 2 =169 180. yes; (-7-5) 2 +(7-12) 2 =169 181. A = 1.125π in 2 /3.53 in 2 182. A=14π / 43.98 ft 2 183. A=27.78π / 87.27 cm 2 184. A=53.13π / 166.9 in 2 185. A=7.77π / 24.4 in 2 186. A=22π / 69.12 ft 2 187. A=72.22π / 226.89 cm 2 188. A=112.5π / 353.43 in 2 189. A=18.06π / 56.72 ft 2 190. A=13.09π / 41.13 m 2 191. A=1.09π / 3.42 cm 2 192. A=57.58π / 180.88 in 2 193. A=50π / 157.08 ft 2 194. A=31.8π / 99.89 m 2 195. A=4.2π / 13.2 cm 2 196. A=220.5π / 692.72 in 2 8. A 9. D 10. C 11. A 12. A 13. C Extended Response 1. 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) 3 3. (a) 110 (b) 8 (c) 55.851 Multiple Choice 1. C 2. C 3. C 4. D 5. A 6. C 7. C Geometry - Circles ~14~ NJCTL.org