# Chapter 12 Practice Test

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1 hapter 12 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. ssume that lines that appear to be tangent are tangent. is the center of the circle. Find the value of. (Figures are not drawn to scale.) Q P a. 291 b. 69 c d is tangent to circle at and to circle at (not drawn to scale). = 7, = 18, and = 5. Find to the nearest tenth. a. 78 b. 39 c. 102 d. 24 a b c d is tangent to circle at. Find the length of the radius r for = 5 and = 8.6. Round to the nearest tenth if necessary. The diagram is not to scale. a. 9.9 b. 7 c. 13 d and are all tangent to (not drawn to scale). J = 9, L = 10, and K = 14. Find the perimeter of. r

2 J a. 66 b. 38 c. 46 d. 33 L K Find the value of. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale P 7 23 a b c. 24 d a. 13 b. 26 c. 77 d a b. 120 c. 5.3 d. 12 a. 8 b. 5 c. 6 d The figure consists of a chord, a secant and a tangent to the circle. Round to the nearest hundredth, if necessary.

3 a b. 9 c d = 20, = 6, and = 8 a b c d a b c. 110 d The circles are congruent. What can you conclude from the diagram?

4 ) ) P F E a. arc arc FE b. arc F arc c. arc arc E d. none of these Use the diagram. is a diameter, and. The figure is not drawn to scale. P 14. Find for = 66. a b. 114 c. 132 d Which statement is NT true? a. arc arc b. c. d. 16. Find m(arc ) for m(arc ) = 43. a. 137 b. 133 c. 86 d The radius of circle is 18, and = 13. Find. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.) a b. 3.8 c d m R = 22. Find m. (The figure is not drawn to scale.)

5 N d a c b Q R a. 68 b. 22 c. 158 d Given that and are right angles and m = 41, what is the measure of arc? (The figure is not drawn to scale.) a. a = 53 b. b = 106 c. c = 73 d. d = If m(arc Y) = 40, what is m Y? (The figure is not drawn to scale.) Y a. 164 b. 303 c. 246 d. 262 a. 140 b. 100 c. 70 d Find the measures of the indicated angles. Which statement is NT true? (The figure is not drawn to scale.) 22. m(arc E) = 96 and m(arc ) = 67. Find m. (The figure is not drawn to scale.)

6 E a b c d Find the value of for m(arc ) = 46 and m(arc ) = 25. (The figure is not drawn to scale.) R S T U a b c. 71 d m S = 36, m(arc RS) = 118, and is tangent to the circle at R. Find m U. (The figure is not drawn to scale.) a. 23 b. 82 c. 46 d Find the diameter of the circle for = 16 and = 28. Round to the nearest tenth. (The diagram is not drawn to scale.) Write the standard equation for the circle. 26. center (2, 7), r = 4 a. ( 7) + (y 2) = 16 b. ( 2) + (y 7) = 4 c. ( 2) + (y 7) = 16 d. ( + 2) + (y + 7) = 4 a. 33 b. 49 c d. 65 a. ( 6) + (y 8) = 10 b. ( 6) + (y 8) = 196 c. ( + 6) + (y + 8) = 14 d. ( + 6) + (y + 8) = center ( 6, 8), that passes through (0, 0)

7 28. The center of a circle is (h, 7) and the radius is 10. The circle passes through (3, 1). Find all possible values of h. a. 8, 7 b. 9, 3 c. 9, 5 d. 10, 3 8 y 29. Find the center and radius of the circle with equation ( + 9) + (y + 5) = 64. a. center (5, 9); r = 8 b. center (9, 5); r = 64 c. center ( 9, 5); r = 64 d. center ( 9, 5); r = low-wattage radio station can be heard only within a certain distance from the station. n the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station can be heard? Short nswer 31. etermine whether a tangent line is shown in the diagram, for = 7, = 3.75, and = 8. Eplain your reasoning. (The figure is not drawn to scale.) a. ( 6) + (y 1) = 32 b. ( + 6) + (y + 1) = 32 c. ( 6) + (y 1) = 16 d. ( + 6) + (y + 1) = 16 b. Is the triangle equilateral, isosceles, or scalene? Eplain. (8 10) P (6) 32. In, NL = NM, and the perimeter is 46 cm.,, and are points of tangency to the circle. M = 4 cm. Find NL. Eplain your reasoning. (The figure is not drawn to scale.) M Q ( ) 34. m = 20 and m(arc ) = 88 (The figure is not drawn to scale.) R N 33. a. Find. (The figure is not drawn to scale.) L a. Find. b. Find y. ) y

8 35. The diameter of a circle has endpoints P( 10, 8) and Q(4, 4). a. Find the center of the circle. b. Find the radius. If your answer is not an integer, epress it in radical form. c. Write an equation for the circle. 36. Graph the circle with equation ( + 1) + (y 3) = 9. ther 37. Show that it is not possible for the lengths of the segments of two intersecting chords to be four consecutive integers. m + 2 m m + 3 m + 1

9 hapter 12 Practice Test nswer Section MULTIPLE HIE 1. NS: TP: 12-1 Eample 1 2. NS: TP: 12-1 Eample 1 3. NS: TP: 12-1 Eample 2 4. NS: TP: 12-1 Eample 3 5. NS: TP: 12-1 Eample 5 6. NS: TP: 12-2 Eample 1 7. NS: TP: 12-2 Eample 3 8. NS: TP: 12-2 Eample 3 9. NS: TP: 12-4 Eample NS: 11. NS: TP: 12-4 Eample NS: TP: 12-4 Eample NS: TP: 12-2 Eample NS: 15. NS: TP: 12-2 Eample NS: TP: 12-2 Eample NS: TP: 12-2 Eample NS: TP: 12-3 Eample NS: TP: 12-3 Eample NS: TP: 12-3 Eample NS: TP: 12-3 Eample NS: TP: 12-4 Eample NS: TP: 12-4 Eample NS: TP: 12-4 Eample NS: TP: 12-4 Eample NS: TP: 12-5 Eample NS: TP: 12-5 Eample NS: 29. NS: TP: 12-5 Eample NS: TP: 12-4 Eample 4 SHRT NSWER 31. NS: No, because. TP: 12-1 Eample NS:

10 and, by the Tangent Theorem, N = N. y subtraction,. lso by the Tangent Theorem, and, so. The perimeter is 46 cm, so. y substitution,, so. Since,, or 19 cm. TP: 12-1 Eample NS: a. 15 b. Scalene; the arc measures are 110, 90, and 160. Since the arcs are not congruent, neither are the chords that intercept them. 34. NS: a. 48 b. 112 TP: 12-4 Eample NS: a. ( 3, 2) b. c. ( + 3) + (y + 2) = NS: y TP: 12-5 Eample 3 THER 37. NS: Let m, m + 1, m + 2, and m + 3 represent the four consecutive numbers. Then the product of the greatest and least numbers will equal the product of the two consecutive middle numbers. Solving the equation m(m + 3) = (m + 1)(m + 2) for m results in m 2 + 3m = m 2 + 3m + 2, or 0 = 2, which is false. TP: 12-4 Eample 3

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