Name: ______________________ Class: _________________ Date: _________ ID: A

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Math 9 Chapter 8 Practice Test

Short Answer

1. O is the centre of this circle and point Q is a point of tangency.Determine the value of t. If necessary, give your answer to the nearest tenth.

2. O is the centre of this circle and point Q is a point of tangency.Determine the values of d and e°. If necessary, give your answers to the nearest tenth.

Name: ______________________ ID: A

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3. O is the centre of this circle. Determine the value of m°.

4. O is the centre of this circle. Determine the value of z°.

5. A circle has radius 8 cm. Which of the following measures could NOT be the length of a chord in the circle: 1 cm, 13 cm, 16 cm, or 19 cm?

6. O is the centre of the circle.Determine the value of x to the nearest tenth, if necessary.

Name: ______________________ ID: A

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7. O is the centre of this circle.Which line is a tangent?

8. O is the centre of the circle.Determine the value of s to the nearest tenth, if necessary.

9. Point O is the centre of this circle. Determine the values of c° and d°.

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10. O is the centre of this circle. Determine the value of g°.

11. O is the centre of the circle.Determine the value of z to the nearest tenth, if necessary.

12. Point O is the centre of this circle. Without solving for a, sketch and label the length of any extra line segments you need to draw to determine the value of a.

Name: ______________________ ID: A

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Problem

13. AC, AE, and CE are tangents to this circle. The points of tangency are: B, F, and DThe circle has radius 16. The distance from the centre of the circle to each vertex of the triangle is: OC = 42, OA = OE = 29Determine the side lengths of ACE, to the nearest tenth.

14. A circle has diameter 38 cm. How far from the centre of the circle, to the nearest centimetre, is a chord 26 cm long?

15. Determine the measure of each interior angle of quadrilateral ABCD.

16. AQ is a tangent to the circle with centre B and to the circle with centre C. The points of tangency are P and Q.Determine the value of y to the nearest tenth.

Name: ______________________ ID: A

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17. Point O is the centre of the circle. Determine the values of x°, y°, and z°.

ID: A

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Math 9 Chapter 8 Practice TestAnswer Section

SHORT ANSWER

1. ANS: 20.9

PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

2. ANS: d = 31.2, e° = 29°

PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

3. ANS: 50°

PTS: 1 DIF: Easy REF: 8.3 Properties of Angles in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

4. ANS: 72°

PTS: 1 DIF: Moderate REF: 8.3 Properties of Angles in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

5. ANS: 19 cm

PTS: 1 DIF: Easy REF: 8.2 Properties of Chords in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

6. ANS: 8.9

PTS: 1 DIF: Moderate REF: 8.2 Properties of Chords in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

7. ANS: PR

PTS: 1 DIF: Easy REF: 8.1 Properties of Tangents to a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

8. ANS: 4.9

PTS: 1 DIF: Moderate REF: 8.2 Properties of Chords in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

ID: A

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9. ANS: c° = 33°, d° = 114°

PTS: 1 DIF: Easy REF: 8.2 Properties of Chords in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

10. ANS: 122°

PTS: 1 DIF: Moderate REF: 8.3 Properties of Angles in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

11. ANS: 4.5

PTS: 1 DIF: Easy REF: 8.2 Properties of Chords in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

12. ANS: Answers may vary. For example:

PTS: 1 DIF: Easy REF: 8.2 Properties of Chords in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

ID: A

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PROBLEM

13. ANS: AC = AB + BCUse the Pythagorean Theorem in OAB and OBC:AB2 = OA2 −OB2

AB2 = 29 2 − 16 2

AB = 29 2 − 16 2

AB =Ö 24.1867…

and BC2 = OC2 −OB2

BC2 = 42 2 − 16 2

BC = 42 2 − 16 2

BC =Ö 38.8329…So, AC =Ö 24.1867…+ 38.8329…

=Ö 63.0196…

AE = AF + FEUse the Pythagorean Theorem in OAF and OEF:AF2 = OA2 −OF2

AF2 = 29 2 − 16 2

AF = 29 2 − 16 2

AF =Ö 24.1867…

and FE 2 = OE 2 −OF2

FE 2 = 29 2 − 16 2

FE = 29 2 − 16 2

FE =Ö 24.1867…So, AE =Ö 24.1867…+ 24.1867…

=Ö 48.3734…

CE = CD + DEUse the Pythagorean Theorem in OCD and ODE:CD2 = OC2 −OD2

CD2 = 42 2 − 16 2

CD = 42 2 − 16 2

CD =Ö 38.8329…

and DE 2 = OE 2 −OD2

DE 2 = 29 2 − 16 2

DE = 29 2 − 16 2

DE =Ö 24.1867…So, CE =Ö 38.8329…+ 24.1867…

=Ö 63.0196…

The triangle has side lengths of about 63, 63, and 48.4.

PTS: 1 DIF: Moderate REF: 8.1 Properties of Tangents to a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Problem-Solving Skills

ID: A

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14. ANS: 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.

Label the known lengths.

PR is a chord of the circle, and OQ is perpendicular to the chord, passing

through the centre of the circle, so PQ = QR and QR is 12

of PR:

QR = 12

(26 cm)

= 13 cm

ST is a diameter of the circle, and OR is a radius of the circle, so OR is 12

of

ST:

ST = 12

(38 cm)

= 19 cmUse the Pythagorean Theorem in OQR.d 2 + 13 2 = 19 2

d 2 = 19 2 − 13 2

d 2 = 192

d = 192

d =Ö 13.8564…So, the chord is approximately 14 cm from the centre of the circle.

PTS: 1 DIF: Moderate REF: 8.2 Properties of Chords in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Conceptual Understanding

ID: A

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15. ANS: AC is a diameter of the circle, so ∠ABC = 90° and ∠ADC = 90°.

The sum of the interior angles of a triangle is 180°. So, in ABC:46° + 90° +∠ACB = 180°

136° +∠ACB = 180°

∠ACB = 180°− 136°

∠ACB = 44°So, ∠BCD = 44° + 27°

= 71°

The sum of the interior angles of a triangle is 180°. So, in ACD:27° + 90° +∠CAD = 180°

117° +∠CAD = 180°

∠CAD = 180°− 117°

∠CAD = 63°So, ∠BAD = 63° + 46°

= 109°

So, the interior angles of quadrilateral ABCD have these measures:∠ABC = 90°, ∠BCD = 71°, ∠ADC = 90°, ∠BAD = 109°

PTS: 1 DIF: Moderate REF: 8.3 Properties of Angles in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Problem-Solving Skills

ID: A

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16. ANS: Use the Pythagorean Theorem in ABP to solve for AP.AP 2 = 18 2 − 6 2

AP = 18 2 − 6 2

AP =Ö 16.9706…

ABP ≅ ACQConsider ACQ as an enlargement of ABP.The scale ratio is: CQBP

= 126

= 2

So, AQ = 2(AP)Then, y = AQ −AP

= 2(AP) −AP

= AP

So, y =Ö 17.0

PTS: 1 DIF: Difficult REF: 8.1 Properties of Tangents to a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Problem-Solving Skills

ID: A

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17. ANS: The sum of the central angles in a circle is 360°.130° + 114° + x° = 360°

244° + x° = 360°

x° = 360°− 244°

x° = 116°

∠ACB is an inscribed angle and ∠AOB is a central angle subtended by the same arc.

So, ∠ACB = 12∠AOB

y° = 12× 116°

y° = 58°

OA and OB are radii, so AOB is isosceles with ∠OAB = ∠OBA = z°.The sum of the angles in a triangle is 180°, so in AOB:z° + z° + 116° = 180°

2z° + 116° = 180°

2z° = 180°− 116°

2z° = 64°

z° = 64°2

z° = 32°

PTS: 1 DIF: Difficult REF: 8.3 Properties of Angles in a CircleLOC: 9.SS1 TOP: Shape and Space (Measurement) KEY: Problem-Solving Skills