GEOMETRY B: CIRCLE TEST PRACTICE
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1 Class: Date: GEOMETRY B: CIRCLE TEST PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the measures of the indicated angles. Which statement is NOT true? (The figure is not drawn to scale.) a. a = 53 b. b = 106 c. c = 73 d. d = A low-wattage radio station can be heard only within a certain distance from the station. On 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? a. (x 6) 2 + (y 1) 2 = 32 c. (x 6) 2 + (y 1) 2 = 16 b. (x + 6) 2 + (y + 1) 2 = 32 d. (x + 6) 2 + (y + 1) 2 = 16 1
2 3. The circles are congruent. What can you conclude from the diagram? a. arc CAB arc FDE c. arc AB arc DE b. arc DF arc AC d. none of these Short Answer 4. Name the minor arc and find its measure. 5. In the circle, m(arc AD) = 82, and m D = 79. Find m DCQ. (The figure is not drawn to scale.) 2
3 6. Find the area of the shaded region. Leave your answer in terms of π and in simplest radical form. 7. If m(arc BY) = 45, what is m YAC? (The figure is not drawn to scale.) 8. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. 3
4 9. FG OP, RS OQ, FG = 20, RS = 32, OP = JK, KL, and LJ are all tangent to O (not drawn to scale). JA = 5, AL = 9, and CK = 15. Find the perimeter of JKL. 12. The circumference of a circle is 44π cm. Find the diameter, the radius, and the length of an arc of
5 13. WZ and XR are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale.) Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.) 14. m P = m O = 152 5
6 Find the circumference. Leave your answer in terms of π m R = 39. Find m O. (The figure is not drawn to scale.) 18. BC is tangent to circle A at B and to circle D at C (not drawn to scale). AB = 9, BC = 30, and DC = 3. Find AD to the nearest tenth. 6
7 19. Name the major arc and find its measure. In the figure, PA scale. and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to 20. For m AOC = 61, find m BPO. 21. For m AOC = 40, find m POB. 22. 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. 7
8 23. BD is tangent to circle O at C, m(arc AEC) = 270, and m ACE = 98. Find m DCE. (The figure is not drawn to scale.) 24. Find the area of the circle. Leave your answer in terms of π. 25. The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Round to the nearest tenth. Write the standard equation for the circle. 26. center ( 8, 6), r = 4 8
9 27. Find the area of the figure to the nearest tenth. 28. Find the center and radius of the circle with equation (x + 10) 2 + (y + 5) 2 = Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. Find the measure of each central angle in the circle graph. a. Sleeping b. Eating Essay 30. Jason designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron used to make the structure. Round the answer to the nearest meter. 9
10 GEOMETRY B: CIRCLE TEST PRACTICE Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: L3 REF: 12-3 Inscribed Angles OBJ: Finding the Measure of an Inscribed Angle NAT: NAEP 2005 G3e ADP K.4 TOP: 12-3 Example 2 KEY: circle inscribed angle intercepted arc inscribed angle-arc relationship 2. ANS: D PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: Finding the Center and Radius of a Circle NAT: NAEP 2005 G4d ADP K.10.4 TOP: 12-4 Example 4 KEY: center circle coordinate plane radius equation of a circle word problem 3. ANS: C PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles NAT: NAEP 2005 G3e ADP K.4 TOP: 12-2 Example 1 KEY: arc central angle congruent circles SHORT ANSWER 4. ANS: arc AB; 115 PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: Central Angles and Arcs NAT: NAEP 2005 M1h ADP K.4 TOP: 10-6 Example 3 KEY: measure of an arc minor arc arc 5. ANS: 60 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: The Angle Formed by a Tangent and a Chord NAT: NAEP 2005 G3e ADP K.4 TOP: 12-3 Example 3 KEY: circle inscribed angle tangent-chord angle intercepted arc arc measure angle measure 6. ANS: Ê ˆ 120π Ë Á m 2 PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: Finding Areas of Circles and Parts of Circles NAT: NAEP 2005 M1h ADP I.4.1 ADP J.1.6 ADP K.4 ADP K.8.2 TOP: 10-7 Example 3 KEY: sector circle area central angle 1
11 7. ANS: 67.5 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: The Angle Formed by a Tangent and a Chord NAT: NAEP 2005 G3e ADP K.4 TOP: 12-3 Example 3 KEY: circle inscribed angle tangent-chord angle intercepted arc arc measure angle measure 8. ANS: 13.9 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Lines Through the Center of a Circle NAT: NAEP 2005 G3e ADP K.4 TOP: 12-2 Example 3 KEY: bisected chords circle perpendicular perpendicular bisector Pythagorean Theorem 9. ANS: 13 PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles NAT: NAEP 2005 G3e ADP K.4 TOP: 12-2 Example 3 KEY: circle radius chord congruent chords right triangle Pythagorean Theorem 10. ANS: 55 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles NAT: NAEP 2005 G3e ADP K.4 TOP: 12-2 Example 1 KEY: arc central angle congruent arcs 11. ANS: 58 PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: Using Multiple Tangents NAT: NAEP 2005 G3e ADP K.4 TOP: 12-1 Example 5 KEY: properties of tangents tangent to a circle triangle 12. ANS: 44 cm; 22 cm; 24.4π cm PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: Circumference and Arc Length NAT: NAEP 2005 M1h ADP K.4 TOP: 10-6 Example 4 KEY: circumference radius 13. ANS: 219 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles NAT: NAEP 2005 G3e ADP K.4 TOP: 12-2 Example 1 KEY: arc central angle congruent arcs arc measure arc addition diameter 2
12 14. ANS: 66 PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e ADP K.4 TOP: 12-1 Example 1 KEY: tangent to a circle point of tangency angle measure properties of tangents central angle 15. ANS: 28 PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e ADP K.4 TOP: 12-1 Example 1 KEY: tangent to a circle point of tangency properties of tangents central angle 16. ANS: 3.7π cm PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: Circumference and Arc Length NAT: NAEP 2005 M1h ADP K.4 TOP: 10-6 Example 4 KEY: circumference diameter 17. ANS: 78 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: Finding the Measure of an Inscribed Angle NAT: NAEP 2005 G3e ADP K.4 TOP: 12-3 Example 2 KEY: circle inscribed angle intercepted arc inscribed angle-arc relationship 18. ANS: 30.6 PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e ADP K.4 TOP: 12-1 Example 2 KEY: tangent to a circle point of tangency properties of tangents Pythagorean Theorem 19. ANS: arc ADB; 310 PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: Central Angles and Arcs NAT: NAEP 2005 M1h ADP K.4 TOP: 10-6 Example 3 KEY: major arc measure of an arc arc 20. ANS: 29 PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: Using Multiple Tangents NAT: NAEP 2005 G3e ADP K.4 TOP: 12-1 Example 4 KEY: properties of tangents tangent to a circle Tangent Theorem 3
13 21. ANS: 40 PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: Using Multiple Tangents NAT: NAEP 2005 G3e ADP K.4 TOP: 12-1 Example 4 KEY: properties of tangents tangent to a circle Tangent Theorem 22. ANS: 9, 3 PTS: 1 DIF: L4 REF: 12-5 Circles in the Coordinate Plane OBJ: Writing an Equation of a Circle NAT: NAEP 2005 G4d ADP K.10.4 KEY: equation of a circle center radius point on the circle algebra 23. ANS: 37 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: The Angle Formed by a Tangent and a Chord NAT: NAEP 2005 G3e ADP K.4 TOP: 12-3 Example 3 KEY: circle inscribed angle tangent-chord angle intercepted arc 24. ANS: 50.41π m 2 PTS: 1 DIF: L2 REF: 10-7 Areas of Circles and Sectors OBJ: Finding Areas of Circles and Parts of Circles NAT: NAEP 2005 M1h ADP I.4.1 ADP J.1.6 ADP K.4 ADP K.8.2 TOP: 10-7 Example 1 KEY: area of a circle radius 25. ANS: 89.8 m 2 PTS: 1 DIF: L3 REF: 10-7 Areas of Circles and Sectors OBJ: Finding Areas of Circles and Parts of Circles NAT: NAEP 2005 M1h ADP I.4.1 ADP J.1.6 ADP K.4 ADP K.8.2 TOP: 10-7 Example 1 KEY: area of a circle radius 26. ANS: (x + 8) 2 + (y 6) 2 = 16 PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: Writing an Equation of a Circle NAT: NAEP 2005 G4d ADP K.10.4 TOP: 12-5 Example 1 KEY: equation of a circle center radius 27. ANS: 20.9 in. 2 PTS: 1 DIF: L2 REF: 10-7 Areas of Circles and Sectors OBJ: Finding Areas of Circles and Parts of Circles NAT: NAEP 2005 M1h ADP I.4.1 ADP J.1.6 ADP K.4 ADP K.8.2 TOP: 10-7 Example 2 KEY: sector circle area 4
14 28. ANS: center ( 10, 5); r = 8 PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: Finding the Center and Radius of a Circle NAT: NAEP 2005 G4d ADP K.10.4 TOP: 12-5 Example 3 KEY: center circle coordinate plane radius 29. ANS: ; 28.8 PTS: 1 DIF: L2 REF: 10-6 Circles and Arcs OBJ: Central Angles and Arcs NAT: NAEP 2005 M1h ADP K.4 TOP: 10-6 Example 1 KEY: central angle circle graph multi-part question word problem problem solving ESSAY 30. ANS: [4] Answers may vary. Sample: The total length of wrought iron used is the sum of the outer circumference plus the inner circumference plus the eleven segments. 1 2 C o C i + 11(1.25) = 1 2 π π (1.25) = 7.5π π = π The length of wrought iron used is approximately 59 meters. [3] correct methods used, but with computational error [2] error in method [1] correct answer with no work shown PTS: 1 DIF: L3 REF: 10-6 Circles and Arcs OBJ: Circumference and Arc Length NAT: NAEP 2005 M1h ADP K.4 TOP: 10-6 Example 5 KEY: circumference concentric circles extended response rubric-based question word problem problem solving 5
![4 TOP: 10-6 Example 1 KEY: central angle circle graph multi-part question word problem problem solving ESSAY 30. ANS: [4] Answers may vary.](/docs-images/47/20640422/images/page_14.jpg "Sample: The total length of wrought iron used is the sum of the outer circumference plus the inner circumference plus the eleven segments. 1 2 C o + 1 2 C i + 11(1.25) = 1 2 π 15 + 1 2 π 13.75 + 11(1.")
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