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NAME___________________________________ DATE__________ PD. ____\ GEOMETRY CHAPTER 10 PRACTICE TEST 1. Identify all chords for circle O. A 10 F H • A G • B 5 r O •O • C • B D • E 2. Identify all tangents for circle O. y F H • A G 6. Give the center and radius of circle A and circle B. Describe the intersection of the two circles and describe all common tangents. 10 • B •O A 10 x –10 • C • B D –10 • E 3. A circle is the set of all points in a plane that _____. 7. Given: ST is tangent to Find RT. R at S [A] have a center [B] are equidistant from a given point [C] have a diameter ) 8. Find m PQ in A. Drawing is not to scale. b2 y − 15g [D] lie within a given radius 4. Define a secant of a circle and illustrate the definition on the circle below. Q P A S 5. AB is tangent to O at A (not drawn to scale). Find the length of the radius r, to the nearest tenth. ° b y + 45g 9. Given: In R ° O, m BAC = 294 ° . Find m ∠ A. NAME___________________________________ DATE__________ PD. ____\ GEOMETRY CHAPTER 10 PRACTICE TEST C 16 5 O B x A [A] 33 ° [A] 16.8 [B] 27 ° [B] 8.1 [C] 16.5 ° [C] 9.4 [D] 13.5 ° [D] 15.2 10. Identify the minor congruent arcs in the figure. B 13. Given: P and PT ⊥ to chord RS at T. Decide whether or not RT = TS. Explain your reasoning. A C 35° 45° 70° D 25° 60° G 55° 70° E 14. Find m ∠ PSQ if m ∠ PSQ = 3 y − 10 and m ∠ PRQ = 2 y + 10 . F 11. Given circle O with radius 34 and OC = 16. Find the measure of AB . A C O Q P B S [A] 10 ° [B] 25 ° 12. Find the value of x. [C] 20 ° R NAME___________________________________ DATE__________ PD. ____\ GEOMETRY CHAPTER 10 PRACTICE TEST [B] 113° [D] 50 ° 15. Given: m ∠ X = 100°; WZ ≅ YZ ; m ∠ Y = 100° X [C] 134° [D] 226° 18. Find the value of x. W Y 7 8 19 Z x Refer to the diagram to find the measure of each of the following: A. ∠ Z B. WZ C. ∠ W D. WX ) ) ) ) 19. Find the length of the missing segment to the nearest tenth. 16. Find the value of x if m AB = 23° and m CD = 41° (not drawn to scale). • 40 D • 9 O C • 10 • ? • x° A 20. Given: m ∠ IED = 94 ° and m ∠ JFG = 97 ° Find the measure of each unknown angle. (not drawn to scale) B ) ) 17. Given: m SQ = 106°, m PR I E = 120° F J 2 Find m ∠ x. 3 D [A] 67° [A] 1 4 G NAME___________________________________ DATE__________ PD. ____\ GEOMETRY CHAPTER 10 PRACTICE TEST m∠1 = 83° , m∠2 = 86° , m∠3 = 94° , m∠4 = 97° A [B] m∠1 = 86° , m∠2 = 83° , m∠3 = 94° , m∠4 = 97° O B [C] m∠1 = 83° , m∠2 = 86° , m∠3 = 97° , m∠4 = 94° [D] m∠1 = 86° , m∠2 = 83° , m∠3 = 97° , m∠4 = 94° D C [A] 35.7 [B] 33.0 21. In the figure shown (not drawn to scale), mBCD = 112° , mDEF = 98° , mFGH = 130° , and mHAB = 20° . Find m ∠FPD . D • C • P• • •A • H • G [D] 55.0 24. Find the equation of the circle of radius 3 with its center at the origin. •E B [C] 16.5 • F [A] 20 ° 25. Find the equation of the circle with center (5, – 2) and radius of 2. 26. Find the length of the leg of this right triangle. LEAVE ANSWER IN SIMPLIFIED RADICAL FORM. 9 a [B] 39 ° [C] 16 ° [D] 92 ° 22. Find the measure of ∠ 1. 7 27. Find the altitude of an isosceles triangle with base 10 and congruent sides of length 9. 28. Given: Rectangle PQRS with QR = 8 and SQ = 10. What is the value of y? 23. Find the diameter of the circle. BC = 11, and DC = 22. Round your answer to the nearest tenth. 29. Find the area of this right triangle if b = 10 and c = 2 41. NAME___________________________________ DATE__________ PD. ____\ GEOMETRY CHAPTER 10 PRACTICE TEST y x 60° c 20 a 37. Find the value of x and y . y b 7 30° 30. A set of Pythagorean triples is _____. x [A] 1, 1, 2 [B] 3, 5, 9 [C] 6, 9, 12 [D] 5, 12, 13 38. Find the value of x, to the nearest whole number. (not drawn to scale) A x 8 28° C B 31. Which set of lengths cannot form a right triangle? [A] 4 mm, 7.5 mm, 8.5 mm 39. Solve the right triangle: α = 40° and a = 17; find β , b, and c [B] 8 mm, 15 mm, 17 mm [C] 16 mm, 30 mm, 34 mm c α b β a [D] 9 mm, 15 mm, 17 mm 32. A triangle has side lengths of 6, 9, and 11. Decide whether it is an acute, right, or obtuse triangle. Explain. 33. Write the ratio of side lengths to hypotenuse in a 45-45-90 right triangle. 34. Write the ratio of side lengths to the hypotenuse in a 30-60-90 right triangle. 35. What is the length of the diagonal of a square with side lengths 7 2? 36. Find the value of x and y. 40. To find the height of a tower, a surveyor positions a transit that is 2 m tall at a spot 55 m from the base of the tower. She measures the angle of elevation to the top of the tower to be 51 ° . What is the height of the tower, to the nearest meter? NAME___________________________________ DATE__________ PD. ____\ GEOMETRY CHAPTER 10 PRACTICE TEST ; CG ≅ EB Reference: [10.1.1.1] [1] AF , AB Reference: [10.1.1.1] Reference: [10.2.2.38] [11] 60 [2] CE Reference: [10.1.1.6] [3] [B] Reference: [10.1.1.12] [4] A secant of a circle is a line that intersects a circle twice. Sketches vary. For example, Reference: [10.2.2.39] [12] [C] Reference: [10.2.2.43] [13] Yes, RT = TS. A diameter that is perpendicular to a chord bisects the chord and its arc (Theorem 10.5). Reference: [10.3.1.50] [14] [D] Reference: [10.1.2.19] [5] 7.5 Reference: [10.1.1.14] [6] The center of circle A is ( –3, 0), and its radius is 2. The center of circle B is ( –3, 6) and its radius is 4. The circles intersect at (–3, 2). The only tangent is the line y = 2. ) Reference: [10.4.2.72] [16] 32° Reference: [10.4.2.75] [17] [B] Reference: [10.1.2.23] [7] 425 = 5 17 ≈ 20.6 Reference: [10.5.1.78] 5 [18] 21 7 Reference: [10.2.1.30] [8] 105 ° Reference: [10.5.2.80] [19] 34.1 Reference: [10.2.1.31] [9] [A] Reference: [10.2.1.37] [10] CD ≅ EF ; BG ≅ FD ≅ EC; BF ≅ GD ≅ DA; AF ≅ DB ) Reference: [10.3.2.56] [15] A. m ∠ Z = 80° B. m WZ = 100° m ∠ W = 80° D. m WX = 100° Reference: [10.3.2.55] [20] [C] Reference: [10.4.2.67] [21] [B] C. NAME___________________________________ DATE__________ PD. ____\ GEOMETRY CHAPTER 10 PRACTICE TEST Reference: [10.4.1.62] [22] 70° Reference: [10.5.2.79] [23] [B] Reference: [9.3.2.34b] [34] 1:1 3 :2 Reference: [9.4.1.42] [35] 14 Reference: [10.6.1.81] [24] x 2 + y 2 = 9 Reference: [9.4.1.46] [36] x = 10, y = 10 3 Reference: [10.6.1.82] 2 2 [25] x − 5 + y + 2 = 4 b g b g Reference: [9.4.1.45] [37] x = 7 3 , y = 14 Reference: [9.2.2.9a] [26] 4 \/ 2 Reference: [9.6.1.77] [38] 17 Reference: [9.2.2.16] [27] 56 or 2 14 Reference: [9.6.1.83] [39] β = 50° Reference: [9.2.2.17] [28] 6 b ≈ 20.26 c ≈ 26.45 Reference: [9.2.2.23] [29] 40 Reference: [9.5.2.72] [40] 70 m Reference: [9.2.2.25] [30] [D] Reference: [9.3.1.29] [31] [D] Reference: [9.3.2.32] [32] Since 62 + 9 2 < 112 , it is an obtuse triangle. Reference: [9.3.2.34a] [33] 1:1: 2