Angles & Arcs Classwork. Geometry Circles ~1~ NJCTL.org. 7. Explain the difference between the radius of a circle and a chord.

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1 Circles Parts of a Circle Classwork 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. Which is longer TC or MA? Justify. 7. Explain the difference between the radius of a circle and a chord. Parts of a Circle Homework Use the diagram of the circle with center C to answer the following: 8. Name the radii 9. Name the chord(s) 10. Name the diameter(s) 11. If CE = 8, what does BD =? 12. If BD = 19, what does CE =? 13. Which is longer DB or AB? Justify. 14. Explain the difference between the diameter of a circle and a chord. Angles & Arcs Classwork In C, AD is the diameter, m BCD = 110 & m ACE = 80. Find the measurement of each arc and classify the arc as a minor arc, major arc, or semicircle. 15. mae 16. mab 17. mabd 18. mebd 19. mbed 20. maed 21. madb Two concentric circles have center P, PS = 6 and SU = Which is greater: mrs or mtu? 23. Which is greater: the length of RS or the length of TU? 24. TPU = 90, how long would chord TU be? Geometry Circles ~1~ NJCTL.org

2 Angles & Arcs Homework In C, AD is the diameter, m BCD = 130 & m ACE = 60. Find the measurement of each arc and classify the arc as a minor arc, major arc, or semicircle. 25. mae 26. mab 27. mabd 28. mebd 29. mbed 30. maed 31. madb Two concentric circles have center P, PS = 3 and SU = Which is greater: mrs or mtu? 33. Which is greater: the length of RS or the length of TU? 34. TPU = 90, how long would chord TU be? Arc Length & Radians Classwork PARCC type Questions In C, AD is the diameter, m BCD = 110, m ACE = 80, and CE = 5, find the following 35. length of AE 36. length of mab 37. length of AD 38. length of EBD 39. length of BED 40. length of ADE 41. length of ADB 42. If the central angle of a circle has measure 60 o and makes a minor arc with length 15, what is the radius? 43. 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? In #44-49, convert the degrees of the angle to radians, or the radians of the angle to degrees. Use 3.14 as your value of π radians radians 49. 3π 2 radians Geometry Circles ~2~ NJCTL.org

3 Arc Length & Radians Homework PARCC type Questions In C, AD is the diameter, m BCD = 130, m ACE = 60, and CE= 8, find the following 50. length of AE 51. length of mab 52. length of AD 53. length of EBD 54. length of BED 55. length of ADE 56. length of ADB 57. If the central angle of a circle has measure 80 o and makes a minor arc with length 12, what is the radius? 58. 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? In #59-64, convert the degrees of the angle to radians, or the radians of the angle to degrees. Use 3.14 as your value of π radians radians 64. π 6 radians Chords, Inscribed Angles & Triangles Class Work Solve for the variable in each problem. C is the center of the circle Geometry Circles ~3~ NJCTL.org

4 (10x - 2) (5x + 2) C PARCC type Questions 82. The figure to the right shows a circle with center H, diameter GF, and inscribed FGJ. HF = 12. Let m GJF = (x + 25) and m JGF = x. a) Find the value of x. J H 12 F G Choose the correct option for each blank. Answer choices are given in the boxes below each blank. b) The length of JF is because. 12 less than 12 greater than 12 JHF is equilateral m JHF < 60 m JHF > Point P is the center of a circle. RT is the diameter of the circle. Point U is a point on the circle, different from R and T. a) Determine if the following statements are always, sometimes, or never true. 1) RT > RU 2) m TRU = 1 (m UPT) 2 3) m RTU = 90 4) m TRU = 2(m RTU) b) If m PUT = 50, what is m RPU? Geometry Circles ~4~ NJCTL.org

5 Chords, Inscribed Angles & Triangles Homework Solve for the variable in each problem. C is the center of the circle C (7x + 3) (3x - 8) Geometry Circles ~5~ NJCTL.org

6 PARCC type Questions 101. The figure to the right shows a circle with center C, diameter BD, and inscribed BDE. BD = 28. Let m BED = (3x) and m EBC = x. a) Find the value of x. Choose the correct option for each blank. Answer choices are given In the boxes below each blank. b) The length of DE is because. 14 less than 14 greater than 14 B ECD is equilateral m ECD < 60 m ECD > 60 E C 28 D 102. Point M is the center of a circle. JK is the diameter of the circle. Point L is a point on the circle, different from J and K. a) Determine if the following statements are always, sometimes, or never true. 1) ML > KL 2) m KJL = 1 (m JKL) 2 3) m KLJ = 90 4) LM = 2(KJ) b) If m JKL = 25, what is m JML? Tangents & Secants Classwork 103. Draw a tangent line to the circle at M What is the difference between a chord and a secant? Draw the common tangents for each set of circles If a circle has a center of (7,6) and is tangent to the x-axis, how big is the radius? 109. If a circle has a center of (7,6) and is tangent to the y-axis, how big is the diameter? Solve for the variable in each problem. C is the center of the circle Geometry Circles ~6~ NJCTL.org

7 PARCC type Question 128. The figure shows two semicircles with centers K & M. The semicircles are tangent to each other at point J, and QN is tangent to both circles at N & O. If KL = JP = 12, what is OQ? O N L K J M P Q Tangents & Secants Homework 129. Draw a tangent line to the circle at A What is the difference between a tangent and a secant? Geometry Circles ~7~ NJCTL.org

8 Draw the common tangents for each set of circles If a circle has a center of (3, -6) and is tangent to the x-axis, how long is the radius? 135. If a circle has a center of (3, -6) and is tangent to the y-axis, how long is the diameter? Solve for the variable in each problem. C is the center of the circle Geometry Circles ~8~ NJCTL.org

9 PARCC type Question 154. The figure shows two semicircles with centers R & S. The semicircles are tangent to each other at point P, and UW is tangent to both circles at V & W. If QR = PT = 18, what is WV? W V Segments & Circles Classwork Q R P Find the value of the variable. C is the center of the circle S T U Segments & Circles Homework Find the value of the variable. C is the center of the circle Geometry Circles ~9~ NJCTL.org

10 Geometry Circles ~10~ NJCTL.org

11 Multiple Choice For questions 1-4, use the diagram at the right of F 1. Name a secant of the circle a. FA b. AC c. BE 2. BF = 7 and tangent BE = 9, what is AE? a b c d d. BC 3. m BCA = 20 and BD = 8, what is the length of BC? a b c d m BCA = 20, what is the measurement of BÂ in radians? a radians b radians c radians d. 2, radians 5. If AB is a diameter and mac = 50, then what is mabc? a. 50 b. 130 c. 230 d Find the value of a. a. 200 b. 300 c. 240 d. 20 a If an angle measures 3 radians, what is its measurement in degrees? a. 30 b c d Find the value of b. a. 70 b. 110 c. 150 d Find the value of c. a. 65 b. 35 c. 30 d. not enough information b 80 Center c 10. Find the value of d. a. 20 b. 40 c. 50 d d Center Geometry Circles ~11~ NJCTL.org

12 11. Find the value of e. a. 7.5 b. 8 c. 8.5 d Find the value of f. a. 2 b. 3 c. 4 d Find the value of g. a. 2 b c. 8 d Find the value of x. a. 3 b c. 9 d. 15 3x + 6 h 5x Point H is the center of a circle. EF is the diameter of the circle. Point G is a point on the circle, different from E and F. 15. EF > HE a. Always b. Sometimes c. Never 16. m EFG = 90 a. Always b. Sometimes c. Never 17. FG = EG a. Always b. Sometimes c. Never 18. m EHG = 2(m EFG) a. Always b. Sometimes c. Never 19. If m FEG = 38, what is m GHF? a. 38 b. 52 c. 76 d. 104 Geometry Circles ~12~ NJCTL.org

13 Extended Response 1. 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 the value of x. b. Find the value of y. c. If AB = 25 and UB (not drawn) = 5, what is the length of AT (not drawn)? 2. In the diagram AB CD and CD is a diameter. a. If mab = 40 find the mbc. b. If AB = 12 and CD = 20, how far from the center is? AB c. Using the information from parts a) and b), how long is ACB? 3. A triangle is inscribed in a circle creating three arcs. Two of the arcs are 80 and 130. a. Draw a diagram for the given information above. b. Find the measurement of the missing arc. c. Find the measurements of all of the inscribed angles and list the angles in order from greatest to least. 4. The figure shows two semicircles with centers D & F. The semicircles are tangent to each other at point C, and BH is tangent to both circles at G & H. DC = CA = 20. a. Determine the lengths of the radii in each circle. Draw additional radii in the diagram. H b. Determine the length of AB. c. Determine the length of GB. G E D C F A B Geometry - Circles ~13~ NJCTL.org

14 1. Segments AT, AM, AC 2. Segments JH, TC 3. Segment TC Segment TC is longer because the diameter is twice the radius. 7. The radius is the segment that has one endpoint as the center of the circle and the other endpoint on the circle. A chord is a segment that has 2 endpoints on the circle. 8. Segments CD, CB, and CE 9. Segments AB, DB 10. Segment DB Segment DB, diameter is longest chord of a circle 14. The diameter is the longest chord and the only chord that passes through the center ; minor ; minor ; semicircle ; major ; major ; semicircle ; major 22. They are equal 23. TU is longer ; minor ; minor ; semicircle ; major ; major ; semicircle ; major 32. They are equal 33. TU is longer Answer Key /π radians radians radians radians radians radians X= degrees degrees 68. X=3 69. X= degrees 71. X= degrees 73. X= degrees degrees degrees 77. X=170 degrees 78. X=20 degrees 79. X= X = 80 degrees 81. x = a) x = 55 b) greater than 12 m JHF > a) 1) Always 2) Always 3) Never 4) Sometimes b) m RPU = v=4 Geometry - Circles ~14~ NJCTL.org

15 85. b= 80 degrees 86. n=220 degrees 87. F=40 degrees 88. R= x=4 90. x= k= d= h=60 degrees 95. g= d= e= n= f = x = a) x = 30 b) 14 ECD is equilateral 102. a) 1) Sometimes 2) Sometimes 3) Always 4) Never b) m JML = Tangent line touches the circle at M 104. A chord has endpoints on the circle, while a secant passes through 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 Two tangent lines on the outsides of the two circles One tangent line at the bottom 108. R= D= x= x= x= c= g= x=2, y= c= x= x= a= k= x= h= f= g= b= m= OQ = 1152 = 24 2 = Tangent line passes through A 130. A tangent touches at one point, while a secant touches at two points 131. Two tangent lines on the outside. Two more tangent lines making a diagonal through the middle One tangent line through the center of the two touching circles. Two more tangent lines, one at the top and one at the bottom No tangent lines 134. R= R= f= t= g= g= x=3; y= j= r= x= d= x=70/ x= degrees degrees 150. x= a=30 degrees 152. d= d=60 degrees 154. WU = 2592 = 36 2 = VU = 648 = 18 2 = WV = = 18 2 = n= x= x= x= x= x= x= x= x= n= r=5 Geometry - Circles ~15~ NJCTL.org

16 166. h= x= y= k= v= x= a=1.66 Extended Response 1. (a) 2 (b) 1.5 (c) 3 2. (a) 110 (b) 8 (c) (a) Note: the letters used in the diagram below can be any random letters chosen. P Unit Review Multiple Choice 1. C 2. C 3. C 4. B 5. D 6. A 7. C 8. C 9. C 10. A 11. D 12. C 13. A 14. A 15. A 16. C 17. B 18. A 19. C O (b) mpo = 150 (c) m OQP = 75 m OPQ = 65 m POQ = (a) E (b) D = 40+x x H 20 Q = 40+x 10+x x = 40 + x 2x = 20 + x x = 20 = AB (c) GB 2 = GB 2 = 900 GB 2 = 800 GB = 20 2 = G C 10 F 10 A x B Geometry - Circles ~16~ NJCTL.org