Review for Grade 9 Math Exam  Unit 8  Circle Geometry


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1 Name: Review for Grade 9 Math Exam  Unit 8  ircle Geometry Date: Multiple hoice Identify the choice that best completes the statement or answers the question. 1. is the centre of this circle and point T is a point of tangency. Determine the value of x. T a) 90 o b) 139 o S 49 x c) 49 o d) 41 o 2. is the centre of this circle and point G is a point of tangency. Determine the value of a. If necessary, give your answer to the nearest tenth. a) 24.5 b) a 22 H c) 17.3 d) 35.6 G 3. is the centre of this circle and point is a point of tangency. Determine the value of m. If necessary, give your answer to the nearest tenth. 17 m a) 28 b) c) 41.7 d) is the centre of the circle. Determine the value of v. a) 26 o b) 52 o c) 64 o d) 38 o 38 v
2 5. is the centre of the circle. Determine the value of a. P a) 49 o b) 20.5 o c) 41 o d) 69.5 o 98 a Q 6. is the centre of the circle. Determine the value of n to the nearest tenth, if necessary. a) 16 b) 4 H n 3 c) 2 d) 5.8 K 5 J 7. is the centre of the circle. Determine the value of z to the nearest tenth, if necessary. L 2 3 M z N a. 4.5 b. 3.6 c. 5 d is the centre of this circle. Identify all the inscribed angles subtended by the minor arc QS. Q a. QS c. QPS and QTS P T S
3 b. PQT and PST d. QPS 9. is the centre of this circle. Determine the value of m. F m 60 a. 30 c. 180 H b. 90 d. 60 G 10. is the centre of this circle. Determine the value of c. T c 94 U a. 180 c. 90 b. 94 d. 47 V 11. is the centre of this circle. Determine the value of z. F z a. 55 c. 90 b. 110 d. 70 D 35 E 12. is the centre of this circle. Determine the value of g. 58 H a. 90 c. 64 b. 58 d. 116 G g J Short nswer
4 13. is the centre of this circle. Which line is a tangent? 14. is the centre of this circle. Point T is a point of tangency. What is the value of e? T e D E 15. Is the line that passes through points U and V a tangent to the circle? U V 16. is the centre of this circle and point is a point of tangency. Determine the values of v and w. v w 17. is the centre of this circle and point S is a point of tangency. Determine the values of m and n. If necessary, give your answers to the nearest tenth.
5 n 39 m R 30 S 50 T 18. is the centre of this circle. Which line segment is a diameter? E D F G 19. Point is the centre of this circle. Without solving for s, sketch and label the lengths of any extra line segments you need to draw to determine the value of s. W s 6 X 4 Y 20. Label the major arc D and the minor arc D of this circle. 21) is the centre of this circle. Is a central angle or an inscribed angle? D
6 22. is the centre of this circle. In this circle, identify the inscribed angle and the central angle subtended by the same minor arc. P Q R 23. Point is the centre of the circle. rc is a semicircle. What is the measure of? 24. is the centre of this circle. Determine the values of y and z. y z 68 D 25. Point is the centre of the circle. Determine the values of y and z. z 76 y Problem 26. Ruppell s Griffon Vulture holds the record for the bird with the highest documented flight altitude. It was spotted at a height of about 11 km above the Earth s surface. The radius of Earth is approximately 6400 km. How far was the vulture from the horizon, H? alculate this distance to the nearest kilometre. H V 11 km 6400 km
7 27. circular mirror with radius 28 cm hangs from a hook. The wire is 48 cm long and is a tangent to the circle at points and. How far, to the nearest tenth, above the top of the mirror is the hook? T 24 cm 28 cm 24 cm 28 cm 28. Draw a point at the centre of this circle. Label the point. How do you know your answer is correct? 29. a) In a circle, can a chord be longer than a diameter of the circle? Explain. b) In a circle, can a chord be shorter than a radius of the circle? Explain. 30. circle has diameter 38 cm. How far from the centre of the circle, to the nearest centimetre, is a chord 26 cm long? 32. Point is the centre of the circle. Determine the values of x, y, and z. z 133 x 107 y
8 Review for Grade 9 Math Exam  Unit 8  ircle Geometry nswer Section MULTIPLE HIE 1. NS: D PTS: 1 DIF: Easy REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 2. NS: D PTS: 1 DIF: Easy REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 3. NS: PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 4. NS: PTS: 1 DIF: Easy REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 5. NS: PTS: 1 DIF: Easy REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 6. NS: PTS: 1 DIF: Easy REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 7. NS: PTS: 1 DIF: Easy REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 8. NS: PTS: 1 DIF: Easy REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 9. NS: PTS: 1 DIF: Easy REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 10. NS: D PTS: 1 DIF: Moderate REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 11. NS: D PTS: 1 DIF: Moderate REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 12. NS: D PTS: 1 DIF: Moderate REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding SHRT NSWER 13. NS: PTS: 1 DIF: Easy REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 14. NS: 90 PTS: 1 DIF: Easy REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding
9 15. NS: Yes. U V PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 16. NS: v = 58, w = 30 PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 17. NS: m = 63.4, n = 60 PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 18. NS: DE PTS: 1 DIF: Easy REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 19. NS: nswers may vary. For example: W 4 3 s X 6 4 Y PTS: 1 DIF: Easy REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding
10 20. NS: D Minor arc D Major arc D PTS: 1 DIF: Easy REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 21. NS: Inscribed angle PTS: 1 DIF: Easy REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 22. NS: Inscribed angle: entral angle: PTS: 1 DIF: Easy REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 23. NS: 180 PTS: 1 DIF: Easy REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 24. NS: y = 68, z = 136 PTS: 1 DIF: Easy REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 25. NS: y = 38, z = 52 PTS: 1 DIF: Moderate REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding
11 PRLEM 26. NS: V H Use the Pythagorean Theorem in solve for HV. to 6400 km 6411 km The vulture was about 375 kilometres from the horizon. PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: ProblemSolving Skills 27. NS: The distance from the centre of the mirror to the hook is: T So, the distance from the top of the mirror to the hook is: T 28 cm Solve for T. So, T 28 cm = cm 28 cm = cm So, the hook is about 8.9 cm above the mirror. PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: ProblemSolving Skills
12 28. NS: I know that the centre of the circle lies along the perpendicular bisector of a chord. So, when two different perpendicular bisectors are drawn, the centre of the circle is the point where they intersect. PTS: 1 DIF: Easy REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: ProblemSolving Skills ommunication 29. NS: a) No. chord joins two points on a circle. Given one point on a circle, the point farthest from that point is on the opposite side of the circle. The line connecting these two points passes through the centre of the circle, so it is a diameter. b) Yes. For example, in this circle, chord is shorter than radius. PTS: 1 DIF: Moderate REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: ProblemSolving Skills ommunication 30. NS: Draw two chords. onstruct the perpendicular bisectors of the chords. The intersection of the perpendicular bisectors is the centre of the circle. PTS: 1 DIF: Moderate REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: ProblemSolving Skills ommunication
13 31. NS: Sketch a diagram. Let d represent the distance from the chord to the centre of the circle. Draw a radius from the centre to one end of the chord. S P 26 cm Q d 38 cm R T Label the known lengths. PR is a chord of the circle, and Q is perpendicular to the chord, passing through the centre of the circle, so PQ = QR and QR is of PR: ST is a diameter of the circle, and R is a radius of the circle, so R is of ST: Use the Pythagorean Theorem in. Q 13 cm R d 19 cm So, the chord is approximately 14 cm from the centre of the circle. PTS: 1 DIF: Moderate REF: 8.2 Properties of hords in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: onceptual Understanding 32. NS: The sum of the central angles in a circle is 360.
14 is an inscribed angle and angle subtended by the same arc. So, is a central z y and are radii, so is isosceles with. The sum of the angles in a triangle is 180, so in : PTS: 1 DIF: Difficult REF: 8.3 Properties of ngles in a ircle L: 9.SS1 TP: Shape and Space (Measurement) KEY: ProblemSolving Skills
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