Geometry - Chapter 12 Test SAMPLE
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1 Class: Date: Geometry - Chapter 12 Test SAMPLE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. a b c. 110 d 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 1
2 3. Write the standard equation of the circle in the graph. a. (x + 3) 2 + (y 2) 2 = 9 c. (x 3) 2 + (y + 2) 2 = 18 b. (x 3) 2 + (y + 2) 2 = 9 d. (x + 3) 2 + (y 2) 2 = 18 Short Answer 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.) 4. m O = m P = 12 2
3 6. BC is tangent to circle A at B and to circle D at C (not drawn to scale). AB = 7, BC = 18, and DC = 5. Find AD to the nearest tenth. 7. AB is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest tenth if necessary. The diagram is not to scale. 8. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 20 inches. The radius of the larger gear is 11 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale. 3
4 9. JK, KL, and LJ are all tangent to O (not drawn to scale). JA = 9, AL = 10, and CK = 14. Find the perimeter of JKL. 10. Pentagon RSTUV is circumscribed about a circle. Solve for x for RS = 10, ST = 13, TU = 11, UV = 12, and VR = 12. The figure is not drawn to scale. 4
5 In the figure, PA scale. and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to 11. For m AOC = 46, find m POB. 12. For m AOC = 50, find m BPO. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. 13. FG OP, RS OQ, FG = 40, RS = 37, OP = 19 5
6 14. NA PA, MO NA, RO PA, MN = 6 feet
7 The figure consists of a chord, a secant and a tangent to the circle. Round to the nearest hundredth, if necessary. 19. AB = 20, BC = 6, and CD = 8 7
8 20. WZ and XR are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale.) Use the diagram. AB is a diameter, and AB CD. The figure is not drawn to scale. 21. Find m CAP for m CBD = Find m(arc BD) for m(arc AC) = 43. 8
9 23. The radius of circle O is 18, and OC = 13. Find AB. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.) 24. If m(arc BY) = 40, what is m YAC? (The figure is not drawn to scale.) 25. m(arc DE) = 96 and m(arc BC) = 67. Find m A. (The figure is not drawn to scale.) 9
10 26. Find the value of x for m(arc AB) = 46 and m(arc CD) = 25. (The figure is not drawn to scale.) 27. Find AB. Round to the nearest tenth if necessary. Write the standard equation for the circle. 28. center (2, 7), r = center ( 6, 8), that passes through (0, 0) 30. Find the center and radius of the circle with equation (x + 9) 2 + (y + 5) 2 =
11 Geometry - Chapter 12 Test SAMPLE Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 REF: 12-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-4 Example 3 KEY: segment length tangent secant 2. ANS: C PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 1 KEY: arc central angle congruent circles 3. ANS: B PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: Finding the Center and Radius of a Circle STA: CA GEOM 7.0 CA GEOM 17.0 TOP: 12-4 Example 4 KEY: center circle coordinate plane radius equation of a circle SHORT ANSWER 4. ANS: 69 OBJ: Using the Radius-Tangent Relationship STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 1 KEY: tangent to a circle point of tangency properties of tangents central angle 5. ANS: 78 OBJ: Using the Radius-Tangent Relationship STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 1 KEY: tangent to a circle point of tangency angle measure properties of tangents central angle 6. ANS: 18.1 OBJ: Using the Radius-Tangent Relationship STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 2 KEY: tangent to a circle point of tangency properties of tangents Pythagorean Theorem 1
12 7. ANS: 7 OBJ: Using the Radius-Tangent Relationship STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 3 KEY: tangent to a circle point of tangency properties of tangents right triangle Pythagorean Theorem 8. ANS: 4.8 inches OBJ: Using the Radius-Tangent Relationship STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 2 KEY: word problem tangent to a circle point of tangency properties of tangents right triangle Pythagorean Theorem 9. ANS: 66 OBJ: Using Multiple Tangents STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 5 KEY: properties of tangents tangent to a circle triangle 10. ANS: 4 PTS: 1 DIF: L3 REF: 12-1 Tangent Lines OBJ: Using Multiple Tangents STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 5 KEY: properties of tangents tangent to a circle pentagon 11. ANS: 46 OBJ: Using Multiple Tangents STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 4 KEY: properties of tangents tangent to a circle Tangent Theorem 12. ANS: 40 OBJ: Using Multiple Tangents STA: CA GEOM 7.0 CA GEOM 21.0 TOP: 12-1 Example 4 KEY: properties of tangents tangent to a circle Tangent Theorem 13. ANS: 20.5 PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 3 KEY: circle radius chord congruent chords right triangle Pythagorean Theorem 2
13 14. ANS: 3 ft PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 2 KEY: circle radius chord congruent chords bisected chords 15. ANS: 77 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 1 KEY: arc central angle congruent arcs 16. ANS: 10 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Lines Through the Center of a Circle STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 3 KEY: bisected chords circle perpendicular perpendicular bisector Pythagorean Theorem 17. ANS: 12 PTS: 1 DIF: L2 REF: 12-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-4 Example 3 KEY: circle chord intersection inside the circle 18. ANS: PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 KEY: circle chord intersection inside the circle intersection outside the circle secant tangent to a circle 19. ANS: 11.5 PTS: 1 DIF: L2 REF: 12-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-4 Example 3 KEY: circle intersection outside the circle secant 20. ANS: 226 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Using Congruent Chords, Arcs, and Central Angles STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 1 KEY: arc central angle congruent arcs arc measure arc addition diameter 3
14 21. ANS: 57 PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Lines Through the Center of a Circle STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 KEY: diameter chord perpendicular angle measure circle right triangle 22. ANS: 137 PTS: 1 DIF: L3 REF: 12-2 Chords and Arcs OBJ: Lines Through the Center of a Circle STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 3 KEY: arc chord-arc relationship diameter chord perpendicular angle measure circle right triangle perpendicular bisector 23. ANS: 24.9 PTS: 1 DIF: L2 REF: 12-2 Chords and Arcs OBJ: Lines Through the Center of a Circle STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-2 Example 3 KEY: bisected chords circle perpendicular perpendicular bisector Pythagorean Theorem 24. ANS: 70 PTS: 1 DIF: L2 REF: 12-3 Inscribed Angles OBJ: The Angle Formed by a Tangent and a Chord STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-3 Example 3 KEY: circle inscribed angle tangent-chord angle intercepted arc arc measure angle measure 25. ANS: 14.5 PTS: 1 DIF: L2 REF: 12-4 Angle Measures and Segment Lengths OBJ: Finding Angle Measures STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-4 Example 1 KEY: circle secant angle measure arc measure intersection outside the circle 26. ANS: 35.5 PTS: 1 DIF: L2 REF: 12-4 Angle Measures and Segment Lengths OBJ: Finding Angle Measures STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-4 Example 1 KEY: circle secant angle measure arc measure intersection inside the circle 4
15 27. ANS: 3.5 PTS: 1 DIF: L3 REF: 12-4 Angle Measures and Segment Lengths OBJ: Finding Segment Lengths STA: CA GEOM 2.0 CA GEOM 7.0 CA GEOM 21.0 TOP: 12-4 Example 3 KEY: circle intersection outside the circle secant tangent 28. ANS: (x 2) 2 + (y 7) 2 = 16 PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: Writing an Equation of a Circle STA: CA GEOM 7.0 CA GEOM 17.0 TOP: 12-5 Example 1 KEY: equation of a circle center radius 29. ANS: (x + 6) 2 + (y + 8) 2 = 100 PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: Writing an Equation of a Circle STA: CA GEOM 7.0 CA GEOM 17.0 TOP: 12-5 Example 2 KEY: equation of a circle center radius point on the circle 30. ANS: center ( 9, 5); r = 8 PTS: 1 DIF: L2 REF: 12-5 Circles in the Coordinate Plane OBJ: Finding the Center and Radius of a Circle STA: CA GEOM 7.0 CA GEOM 17.0 TOP: 12-5 Example 3 KEY: center circle coordinate plane radius 5
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