Name: Date: 1. In circle P, XY is a. 4. How many radii can be named in the diagram? A. radius. diameter A. 2. 3 C. 4 D. 5 C. chord D. circumference 2. In circle P, A is a. A. diameter. radius C. circumference D. chord 5. Which of the following is not a radius of the circle? 3. Which of the following circles are tangent? A.. C. D. A and F C and E D and C AC and DF A.. C. D. page 1
6. Which answer names a chord of circle O? A. DE. AO 9. In the accompanying diagram, PC is tangent to circle O, PA is a secant, PC = 6, and P = 3. Find A. C. CO D. DE 7. In the accompanying diagram, PA is tangent to circle O at A. If C = 12 and P = 4, what is the length of PA? A. 4 3. 48 C. 16 3 D. 8 10. In the accompanying figure, AD is tangent to circle O at D and AC is a secant. If AD = 4 and AC = 8, find A. 8. In the accompanying diagram, tangent A and secant ACD are drawn to circle O from point A. If AC = 4 and CD = 12, find A. page 2
11. In the accompanying diagram of circle O, chord CD bisects chord A at E, CE = 2, and A = 8. Find ED. 14. In the accompanying diagram, chords A and CD of circle O intersect at E. If AE = x, E = x 6, and CE = ED = 4, find AE. 12. In the accompanying diagram of circle O, chords A and CD intersect at point E. If AE = 2, CD = 9, and CE = 4, find E. 15. In the accompanying figure, chords A and CD intersect at E. If CD = 11, E = 4, and CE = 3, find AE. 13. In the accompanying diagram of circle O, chords A and CD intersect at E. If AE = 3, E = 4, CE = x, and ED = x + 1, find CE. 16. In the accompanying diagram of circle O, chords A and CD intersect at E. If AE = 4, E = 6, and CE = 3, find ED. page 3
17. In the accompanying diagram, circle O is inscribed in AC so that the circle is tangent to A at F, to C at E, and to AC at D. If AF = F = 5 and DC = 7, find the perimeter of AC. 20. In the accompanying diagram, segments RS, ST, and TR are tangent to circle O at A,, and C, respectively. If S = 3, T = 5, and TR = 13, what is the measure of RS? 18. In the accompanying diagram, PA and PCD are externally tangent to circles O and O. If P = 16 and CD = 10, find PA. 21. In the accompanying diagram, A is tangent to circle O at A. Radii OA and OC are drawn, and OC is extended to intersect A at. If A = 15 and O = 17, find the measure of a radius of circle O. 19. In the accompanying diagram, AF, AEC, and GC are tangent to circle O at F, E, and G, respectively. If A = 32, AE = 20, and EC = 24, find C. page 4
22. The accompanying diagram shows two intersecting paths within a circular garden. 24. In the diagram below of circle O, chords A and CD intersect at E. What is the length of the portion of the path marked x? If m AEC = 34 and mac = 50, what is md? A. 16. 18 C. 68 D. 118 A. 8 1 3. 11 C. 3 D. 12 23. In the diagram below of circle O, chords AD and C intersect at E, mac = 87, and md = 35. 25. In the diagram below of circle O, chords AE and DC intersect at point, such that mac = 36 and mde = 20. What is the degree measure of CEA? A. 87. 61 C. 43.5 D. 26 What is m AC? A. 56. 36 C. 28 D. 8 page 5
26. In the diagram of circle O below, chord CD is parallel to diameter AO and mac = 30. 28. In circle O shown in the diagram below, chords A and CD are parallel. What is mcd? A. 150. 120 C. 100 D. 60 If ma = 104 and mcd = 168, what is m D? A. 38. 44 C. 88 D. 96 27. In the diagram below of circle O, chord A is parallel to chord CD. 29. In the diagram below, two parallel lines intersect circle O at points A,, C, and D, with ma = x + 20 and mdc = 2x 20. Find ma. Which statement must be true? A. C. AC = D. A = CD D. A = CD AD = CD page 6
30. In the accompanying figure, the measure of angle AO is 50. Find the measure of inscribed angle AC. 33. In the accompanying diagram, A is a diameter of circle O and chord CD intersects diameter A at E. If mad = 100 and mac = 40, find m DE. 31. In the accompanying diagram, mc = 120. Find the measure of inscribed angle AC. 34. In the accompanying diagram, chords A and CD intersect in the circle at E. mad = 80, find m AEC. If mc = 60 and 32. In the accompanying figure, the measure of minor arc A is 100. Find the measure of inscribed angle AC. 35. In the diagram below, chords A and CD intersect at E. If m AEC = 4x, mac = 120, and md = 2x, what is the value of x? A. 12. 20 C. 30 D. 60 page 7
36. In the accompanying diagram, PA and PCD are secants to the circle. If m P = 40 and mad = 120, find mc. 39. In the accompanying diagram, A is tangent to circle O at and ACD is a secant. If m A = 40 and md = 140, find mc. 37. In the accompanying diagram, tangent PA and secant PC are drawn to circle O from point P. If mac = 80 and ma = 60, what is the measure of P? 40. In the accompanying diagram of circle O, the measure of inscribed angle AC is 40. Find, in degrees, the measure of central angle OC. A. 10. 20 C. 60 D. 70 38. In the diagram below, PA is tangent to the circle at A and PC is a secant. If ma = 80 and mc = 100, what is m AP? 41. In the accompanying diagram of circle O, ma = 64 and m AE = 52. What is the measure of CD? A. 104. 80 C. 52 D. 40 page 8
42. In the accompanying diagram, PQ is tangent to circle O at Q and PRT is a secant. If P = 56 and mqt = 192, find mqr. 44. In the accompanying diagram, A is a diameter and mc = 50. Find m CA. 43. In the accompanying diagram, AC is inscribed in circle O and A is a diameter. 45. A dog has a 20-foot leash attached to the corner where a garage and a fence meet, as shown in the accompanying diagram. When the dog pulls the leash tight and walks from the fence to the garage, the arc the leash makes is 55.8 feet. What is the number of degrees in m C? A. 30. 45 C. 60 D. 90 What is the measure of angle θ between the garage and the fence, in radians? A. 0.36. 2.79 C. 3.14 D. 160 page 9
46. The accompanying diagram shows the path of a cart traveling on a circular track of radius 2.40 meters. The cart starts at point A and stops at point, moving in a counterclockwise direction. What is the length of minor arc A, over which the cart traveled, to the nearest tenth of a meter? 48. In the diagram below of circle C, mqt = 140 and m P = 40. What is mrs? A. 50. 60 C. 90 D. 100 47. A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle AC measuring 1 radian and radius A = 20 feet. 49. In the diagram below of circle O, chord A bisects chord CD at E. If AE = 8 and E = 9, find the length of CE in simplest radical form. What is the length of arc AC, in feet? A. 63. 31 C. 20 D. 10 page 10
50. In the diagram of circle O below, chords A and CD are parallel, and D is a diameter of the circle. 52. In the accompanying diagram of circle O, chord A is parallel to chord CD. If mac = 100, find m OD. If mad = 60, what is m CD? A. 20. 30 C. 60 D. 120 53. In the accompanying figure, central angle AOC measures 60. What is the number of degrees in the measure of inscribed angle AC? 51. In the accompanying diagram of circle O, chords A and CD intersect at E and AD is a diameter. If mc = 82, find m AED. 54. In the accompanying diagram of circle O, A CD, C is a diameter, and radius AO is drawn. If m AC = 20, find md. page 11
55. In the circle shown, chords AC and D intersect at E. If E = x 4, DE = 2x + 9, AE = x, and EC = x + 6. How long is AC? 56. O is the center of each circle. Find x in each of I, II, III respectively. A. 18. 21 C. 22 D. 24 A. 2 161, 657, 2 39. 34, 15, 2 39 C. 2 161, 15, 2 39 D. 34, 15, 2 89 page 12
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