Math 9 Unit 8: Circle Geometry Pre-Exam Practice

Size: px
Start display at page:

Download "Math 9 Unit 8: Circle Geometry Pre-Exam Practice"

Transcription

1 Math 9 Unit 8: Circle Geometry Pre-Exam Practice Name: 1. A 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? Calculate this distance to the nearest kilometre. H V 11 km 6400 km 2. AC, AE, and CE are tangents to this circle. The points of tangency are: B, F, and D. The circle has radius 11. The distance from the centre of the circle to each vertex of the triangle is: C = 34, A = E = 19 Determine the side lengths of ACE, to the nearest tenth. A B F C D E 3. 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. C 12 B 18 6 Q y P A 4. A circle has diameter 32 cm. How far from the centre of the circle, is a chord 20 cm long? 5. A pedestrian underpass is constructed using a cylindrical pipe of radius 2.6 m. The bottom of the pipe will be filled and paved. The headroom at the centre of the path is 3.9 m. How wide is the path to the nearest tenth of a metre? 2.6 m 3.9 m

2 6. Determine the values of x and y. What can you say about line segment AD? A B 53 y 37 C x D 7. Point is the centre of the circle. Determine the values of x, y, and z. A z 133 x 107 B y C 8. Circle C has two chords drawn in it. Chord XY is 9.3 cm long and chord YZ is 12.4 cm long. When X and Z are joined by a straight line, the line runs through the centre of the circle. What is the diameter of the circle? Sketch and label the scenario. Justify your calculations. 9. Circle C has two inscribed angles measuring 42 and 36. What is the measure of STU, TUV and SRT? 10. The diagram shown below is a semicircle with inscribed angles. Point C is the centre point of the complete circle. What is the measure of DBE, BDE and ADB? 11. The radius of a circle is 90 mm long and passes through the centre of a chord at a distance of 46 mm from the circumference of the circle. What is the length of the chord to the nearest hundredth? Show your thinking.

3 12. A circular garden has a diameter of 6 m. There is a tree planted in the centre. David wants to build a wall in the garden. He needs to build the wall so that the distance from the edge of the garden to the centre of the wall is of the distance from the centre of the garden to the edge of the garden. Determine the length of the wall, to the nearest tenth, if both ends touch the edge of the garden. 13. Circle C has a diameter of 100 mm. What is the measure of the chord AB? Express your answer to the nearest whole millimetre. 14. Determine the length of chord PR in the figure below. Show your work, to the nearest whole millimetre. 15. In the figure shown, what is the measure of PS? 16. In the figure below, line QP is a tangent to the circle, and has a length of 21 cm. Line Q runs from the centre of the circle to the end of the tangent and is 35 cm long. What is the diameter of the circle?

4 17. Given the information in the diagram, what is the measure of the diameter of the circle? 18. Ravinder is flying a model plane at the end of a tether. The plane breaks off the tether at point A and lands 24 m away at point B. How far is the plane from Ravinder? Justify your response. 19. A round dining table has a centre, H, and a diameter of 1.2 m. The table is pushed into a corner of a dining room, as shown. Determine the distance between the corner of the wall, C, and the edge of the table. Express your answer to the nearest millimetre. 20. Four round patio stones are placed together as shown. Each patio stone has a diameter of 30 cm. What would be the size of the largest possible square tile that could be placed in the middle of the arrangement of patio stones? Express your answer to the nearest centimetre.

5 Answer Section 1. ANS: V H Use the Pythagorean Theorem in solve for HV. to 6400 km 6411 km The vulture was about 375 kilometres from the horizon. 2. ANS: AC = AB + BC Use the Pythagorean Theorem in AB and BC: and So, AE = AF + FE Use the Pythagorean Theorem in AF and EF: and So, CE = CD + DE Use the Pythagorean Theorem in CD and DE:

6 and So, 3. ANS: Use the Pythagorean Theorem in to solve for AP. Consider as an enlargement of. The scale ratio is: So, AQ = 2(AP) Then, So, y 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. S P 20 cm Q d 32 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:

7 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 10 cm R d 16 cm So, the chord is approximately 12 cm from the centre of the circle. 5. ANS: Draw a radius from the centre of the pipe,, to an edge of the path, E. Label the midpoint of the path F. E is a radius, so: E = 2.6 m Use the Pythagorean Theorem in solve for EF. to E 2.6 m 1.3 m F The width of the path is twice the length of EF. So, the width of the path is about 4.5 m. 6. ANS: Since and are inscribed angles subtended by the same arc AB, they are congruent. x = 37 The sum of the interior angles of a triangle is 180. So, in :

8 Since arc AD subtends right, arc AD is a semicircle and line segment AD is a diameter of the circle. 7. ANS: The sum of the central angles in a circle is 360. is an inscribed angle and angle subtended by the same arc. So, is a central A z B y A and B are radii, so is isosceles with. The sum of the angles in a triangle is 180, so in : C 8. ANS: Since line XZ runs through the centre of the circle, XZ is a diameter. XYZ is 90º. Using the Pythagorean theorem, the length of XZ The diameter of the circle is 15.5 cm.

9 9. ANS: a) STU and SVU are both subtended by arc SU. Therefore, SVU = STU. STU is 36. b) TUV and TSV are both subtended by arc VT. Therefore, TUV = TSV. TUV is 42. c) STU, TSV, and SRT form a triangle. SRT = 180 ( ) = 102 SRT is ANS: a) DBE and DAE are both subtended by arc DE. Therefore, DBE = DAE. DBE is 35. b) BDE and BAE are both subtended by arc BE. Therefore, BDE = BAE. BDE is 30. c) ADB is subtended by diameter AB. ADB is ANS: Chord MN has a length of mm. 12. ANS: Diameter of garden = 6 m Radius of garden = 3 m Length of VZ = = 1.8 m Length UZ = = 1.2 m Triangle UYZ has a hypotenuse of 3 m and one side 1.2 m long.

10 Length of wall is The wall is approximately 5.5 m long. 13. ANS: The length of chord AB is approximately 71 mm. 14. ANS: NPQ is a right angled triangle. PR = PQ (Both are legs of an equilateral triangle.)

11 PR = 48 mm Chord PR is 48 mm long. 15. ANS: PQ = 90 PQ = 180 (90 56 = 34 Since PS is an isosceles triangle, SP = PS, so PS is 17 PS is ANS: Line P is a radius of the circle. Diameter = 2(radius) = 2 (28) = 56 cm The diameter of circle is 56 cm. 17. ANS: Radius = T Diameter = 2 48 = 96 The diameter of the circle is 96 mm. 18. ANS: The plane lands 30 m away from Ravinder.

12 19. ANS: The distance from the corner of the dining room to the edge of the table is approximately 249 mm. 20. ANS: he largest possible square tile would measure 12 cm by 12 cm.

Review for Grade 9 Math Exam - Unit 8 - Circle Geometry

Review for Grade 9 Math Exam - Unit 8 - Circle Geometry 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

More information

Ch 10 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Ch 10 Review. Multiple Choice Identify the choice that best completes the statement or answers the question. Ch 10 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram shown, the measure of ADC is a. 55 b. 70 c. 90 d. 180 2. What is the measure

More information

Math 9 Chapter 8 Practice Test

Math 9 Chapter 8 Practice Test Name: Class: Date: ID: A 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

More information

1. Draw and label a diagram to illustrate the property of a tangent to a circle.

1. Draw and label a diagram to illustrate the property of a tangent to a circle. Master 8.17 Extra Practice 1 Lesson 8.1 Properties of Tangents to a Circle 1. Draw and label a diagram to illustrate the property of a tangent to a circle. 2. Point O is the centre of the circle. Points

More information

SM2H Unit 6 Circle Notes

SM2H Unit 6 Circle Notes Name: Period: SM2H Unit 6 Circle Notes 6.1 Circle Vocabulary, Arc and Angle Measures Circle: All points in a plane that are the same distance from a given point, called the center of the circle. Chord:

More information

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.

More information

Solve problems involving tangents to a circle. Solve problems involving chords of a circle

Solve problems involving tangents to a circle. Solve problems involving chords of a circle 8UNIT ircle Geometry What You ll Learn How to Solve problems involving tangents to a circle Solve problems involving chords of a circle Solve problems involving the measures of angles in a circle Why Is

More information

Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.

Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. April 9, 01 Standards: MM1Ga, MM1G1b Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? (1,10) B. (,7) C. (,) (,) (,1). Points P, Q, R, and S lie on a line

More information

Pre-Test. Use the following figure to answer Questions 1 through 6. B C. 1. What is the center of the circle? The center of the circle is point G.

Pre-Test. Use the following figure to answer Questions 1 through 6. B C. 1. What is the center of the circle? The center of the circle is point G. Pre-Test Name Date Use the following figure to answer Questions 1 through 6. A B C F G E D 1. What is the center of the circle? The center of the circle is point G. 2. Name a radius of the circle. A radius

More information

2016 State Mathematics Contest Geometry Test

2016 State Mathematics Contest Geometry Test 2016 State Mathematics Contest Geometry Test In each of the following, choose the BEST answer and record your choice on the answer sheet provided. To ensure correct scoring, be sure to make all erasures

More information

C=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle

C=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle 10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by

More information

Geometry Honors Homework

Geometry Honors Homework Geometry Honors Homework pg. 1 12-1 Practice Form G Tangent Lines Algebra Assume that lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. 2. 3. The circle

More information

Intermediate Math Circles Wednesday October Problem Set 3

Intermediate Math Circles Wednesday October Problem Set 3 The CETRE for EDUCTI in MTHEMTICS and CMPUTIG Intermediate Math Circles Wednesday ctober 24 2012 Problem Set 3.. Unless otherwise stated, any point labelled is assumed to represent the centre of the circle.

More information

Indicate whether the statement is true or false.

Indicate whether the statement is true or false. PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.

More information

10.1 Tangents to Circles. Geometry Mrs. Spitz Spring 2005

10.1 Tangents to Circles. Geometry Mrs. Spitz Spring 2005 10.1 Tangents to Circles Geometry Mrs. Spitz Spring 2005 Objectives/Assignment Identify segments and lines related to circles. Use properties of a tangent to a circle. Assignment: Chapter 10 Definitions

More information

Meet #4. Math League SCASD. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):

Meet #4. Math League SCASD. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets): Math League SCASD Meet #4 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Properties of Circles 3. Number Theory: Modular Arithmetic,

More information

0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.

0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below. Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would

More information

1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.

1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)

More information

Name. 9. Find the diameter and radius of A, B, and C. State the best term for the given figure in the diagram.

Name. 9. Find the diameter and radius of A, B, and C. State the best term for the given figure in the diagram. Name LESSON 10.1 State the best term for the given figure in the diagram. 9. Find the diameter and radius of A, B, and C. 10. Describe the point of intersection of all three circles. 11. Describe all the

More information

Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.

Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement. Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12

More information

Unit 10 Geometry Circles. NAME Period

Unit 10 Geometry Circles. NAME Period Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference

More information

Maharashtra State Board Class X Mathematics - Geometry Board Paper 2016 Solution

Maharashtra State Board Class X Mathematics - Geometry Board Paper 2016 Solution Maharashtra State Board Class X Mathematics - Geometry Board Paper 016 Solution 1. i. ΔDEF ΔMNK (given) A( DEF) DE A( MNK) MN A( DEF) 5 5 A( MNK) 6 6...(Areas of similar triangles) ii. ΔABC is 0-60 -90

More information

Properties of the Circle

Properties of the Circle 9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference

More information

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

More information

0114ge. Geometry Regents Exam 0114

0114ge. Geometry Regents Exam 0114 0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?

More information

Side c is called the hypotenuse. Side a, and side b, are the other 2 sides.

Side c is called the hypotenuse. Side a, and side b, are the other 2 sides. 8.1 Properties of Tangents to a Circle Recall: Theorem of Pythagoras Side c is called the hypotenuse. Side a, and side b, are the other 2 sides. b Recall: Angle Sum Property In any triangle, the angles

More information

0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC? 0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

More information

Lesson 2B: Thales Theorem

Lesson 2B: Thales Theorem Lesson 2B: Thales Theorem Learning Targets o I can identify radius, diameter, chords, central circles, inscribed circles and semicircles o I can explain that an ABC is a right triangle, then A, B, and

More information

Geometry Final Exam REVIEW

Geometry Final Exam REVIEW Name: Class: _ Date: _ Geometry Final Exam 09-10 - REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the perimeter and area of the parallelogram.

More information

Ready To Go On? Skills Intervention 11-1 Lines That Intersect Circles

Ready To Go On? Skills Intervention 11-1 Lines That Intersect Circles Name ate lass STION 11 Ready To Go On? Skills Intervention 11-1 Lines That Intersect ircles ind these vocabulary words in Lesson 11-1 and the Multilingual Glossary. Vocabulary interior of a circle exterior

More information

BOARD QUESTION PAPER : MARCH 2016 GEOMETRY

BOARD QUESTION PAPER : MARCH 2016 GEOMETRY BOARD QUESTION PAPER : MARCH 016 GEOMETRY Time : Hours Total Marks : 40 Note: (i) Solve All questions. Draw diagram wherever necessary. (ii) Use of calculator is not allowed. (iii) Diagram is essential

More information

What You ll Learn. Why It s Important. We see circles in nature and in design. What do you already know about circles?

What You ll Learn. Why It s Important. We see circles in nature and in design. What do you already know about circles? We see circles in nature and in design. What do you already know about circles? What You ll Learn ircle properties that relate: a tangent to a circle and the radius of the circle a chord in a circle, its

More information

Circle Geometry. This booklet belongs to:

Circle Geometry. This booklet belongs to: Circle Geometry This booklet belongs to: LESSON # DATE QUESTIONS FROM NOTES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Questions that I find difficult Find

More information

0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.

0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism. 0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD

More information

Unit 1. GSE Analytic Geometry EOC Review Name: Units 1 3. Date: Pd:

Unit 1. GSE Analytic Geometry EOC Review Name: Units 1 3. Date: Pd: GSE Analytic Geometry EOC Review Name: Units 1 Date: Pd: Unit 1 1 1. Figure A B C D F is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, 1). 2 Which statement is true?

More information

Mid-Chapter Quiz: Lessons 10-1 through Refer to. 1. Name the circle. SOLUTION: The center of the circle is A. Therefore, the circle is ANSWER:

Mid-Chapter Quiz: Lessons 10-1 through Refer to. 1. Name the circle. SOLUTION: The center of the circle is A. Therefore, the circle is ANSWER: Refer to. 1. Name the circle. The center of the circle is A. Therefore, the circle is 2. Name a diameter. ; since is a chord that passes through the center, it is a diameter. 3. Name a chord that is not

More information

MT - w A.P. SET CODE MT - w - MATHEMATICS (71) GEOMETRY- SET - A (E) Time : 2 Hours Preliminary Model Answer Paper Max.

MT - w A.P. SET CODE MT - w - MATHEMATICS (71) GEOMETRY- SET - A (E) Time : 2 Hours Preliminary Model Answer Paper Max. .P. SET CODE.. Solve NY FIVE of the following : (i) ( BE) ( BD) ( BE) ( BD) BE D 6 9 MT - w 07 00 - MT - w - MTHEMTICS (7) GEOMETRY- (E) Time : Hours Preliminary Model nswer Paper Max. Marks : 40 [Triangles

More information

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2) 10. Circles Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular

More information

( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x 2 = - 8y.

( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x 2 = - 8y. PROBLEMS 04 - PARABOLA Page 1 ( 1 ) Find the co-ordinates of the focus, length of the latus-rectum and equation of the directrix of the parabola x - 8. [ Ans: ( 0, - ), 8, ] ( ) If the line 3x 4 k 0 is

More information

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true? 0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100

More information

Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems

Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary

More information

New Jersey Center for Teaching and Learning. Progressive Mathematics Initiative

New Jersey Center for Teaching and Learning. Progressive Mathematics Initiative Slide 1 / 150 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students

More information

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ

More information

Label carefully each of the following:

Label carefully each of the following: Label carefully each of the following: Circle Geometry labelling activity radius arc diameter centre chord sector major segment tangent circumference minor segment Board of Studies 1 These are the terms

More information

Chapter 18 Exercise 18.1

Chapter 18 Exercise 18.1 hapter 18 Eercise 18.1 Q. 1. (i) 180 37 = 143 ( = 143 ) (ii) 180 117 = 63 ( = 63 ) 180 90 = 90 (y = 90 ) (iii) + + 3 + 45 = 180 4.5 = 135 (iv) 180 90 = y 90 = y = 30 45 = y 66 + ( + y) + 47 = 180 + y =

More information

So, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x.

So, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x. ALGEBRA Find the value of x. 1. Arc ST is a minor arc, so m(arc ST) is equal to the measure of its related central angle or 93. and are congruent chords, so the corresponding arcs RS and ST are congruent.

More information

0609ge. Geometry Regents Exam AB DE, A D, and B E.

0609ge. Geometry Regents Exam AB DE, A D, and B E. 0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible

More information

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite

More information

Math & 8.7 Circle Properties 8.6 #1 AND #2 TANGENTS AND CHORDS

Math & 8.7 Circle Properties 8.6 #1 AND #2 TANGENTS AND CHORDS Math 9 8.6 & 8.7 Circle Properties 8.6 #1 AND #2 TANGENTS AND CHORDS Property #1 Tangent Line A line that touches a circle only once is called a line. Tangent lines always meet the radius of a circle at

More information

Circle Geometry. What You'll Learn. Why It's Important. in design. about circles?

Circle Geometry. What You'll Learn. Why It's Important. in design. about circles? Circle Geometry We see circles in n i iture and in design. What do you aire a ly know about circles? What You'll Learn Cir< le properties that relate: a tan( ent to a circle and the radius < f the circle

More information

Plane geometry Circles: Problems with some Solutions

Plane geometry Circles: Problems with some Solutions The University of Western ustralia SHL F MTHMTIS & STTISTIS UW MY FR YUNG MTHMTIINS Plane geometry ircles: Problems with some Solutions 1. Prove that for any triangle, the perpendicular bisectors of the

More information

ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS.

ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS. ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS. A B X Z Y A MINOR arc is LESS than 1/2 way around the circle. A MAJOR arc is MORE than 1/2 way around

More information

( ) ( ) Geometry Team Solutions FAMAT Regional February = 5. = 24p.

( ) ( ) Geometry Team Solutions FAMAT Regional February = 5. = 24p. . A 6 6 The semi perimeter is so the perimeter is 6. The third side of the triangle is 7. Using Heron s formula to find the area ( )( )( ) 4 6 = 6 6. 5. B Draw the altitude from Q to RP. This forms a 454590

More information

Park Forest Math Team. Meet #4. Geometry. Self-study Packet

Park Forest Math Team. Meet #4. Geometry. Self-study Packet Park Forest Math Team Meet #4 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. : ngle measures in plane figures including supplements and complements 3. Number Theory:

More information

Geometry 3 SIMILARITY & CONGRUENCY Congruency: When two figures have same shape and size, then they are said to be congruent figure. The phenomena between these two figures is said to be congruency. CONDITIONS

More information

2012 Canadian Senior Mathematics Contest

2012 Canadian Senior Mathematics Contest The CENTRE for EDUCATION in ATHEATICS and COPUTING cemc.uwaterloo.ca 01 Canadian Senior athematics Contest Tuesday, November 0, 01 (in North America and South America) Wednesday, November 1, 01 (outside

More information

Edexcel New GCE A Level Maths workbook Circle.

Edexcel New GCE A Level Maths workbook Circle. Edexcel New GCE A Level Maths workbook Circle. Edited by: K V Kumaran kumarmaths.weebly.com 1 Finding the Midpoint of a Line To work out the midpoint of line we need to find the halfway point Midpoint

More information

G.C.B.5: Arc Length 1

G.C.B.5: Arc Length 1 Regents Exam Questions G.C.B.5: Arc Length 1 www.jmap.org Name: G.C.B.5: Arc Length 1 1 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian

More information

Time : 2 Hours (Pages 3) Max. Marks : 40. Q.1. Solve the following : (Any 5) 5 In PQR, m Q = 90º, m P = 30º, m R = 60º. If PR = 8 cm, find QR.

Time : 2 Hours (Pages 3) Max. Marks : 40. Q.1. Solve the following : (Any 5) 5 In PQR, m Q = 90º, m P = 30º, m R = 60º. If PR = 8 cm, find QR. Q.P. SET CODE Q.1. Solve the following : (ny 5) 5 (i) (ii) In PQR, m Q 90º, m P 0º, m R 60º. If PR 8 cm, find QR. O is the centre of the circle. If m C 80º, the find m (arc C) and m (arc C). Seat No. 01

More information

Name Date Period Notes Formal Geometry Chapter 8 Right Triangles and Trigonometry 8.1 Geometric Mean. A. Definitions: 1.

Name Date Period Notes Formal Geometry Chapter 8 Right Triangles and Trigonometry 8.1 Geometric Mean. A. Definitions: 1. Name Date Period Notes Formal Geometry Chapter 8 Right Triangles and Trigonometry 8.1 Geometric Mean A. Definitions: 1. Geometric Mean: 2. Right Triangle Altitude Similarity Theorem: If the altitude is

More information

Geometry Honors Final Exam Review June 2018

Geometry Honors Final Exam Review June 2018 Geometry Honors Final Exam Review June 2018 1. Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle. 2. Casey has a 13-inch television and a 52-inch television

More information

Chapter 3 Cumulative Review Answers

Chapter 3 Cumulative Review Answers Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The

More information

MEMO MATHEMATICS: PAPER II

MEMO MATHEMATICS: PAPER II MEMO CLUSTER PAPER 2016 MATHEMATICS: PAPER II Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 28 pages and an Information Sheet of 2 pages(i-ii).

More information

Circles. Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: Angles & Arcs Class Work

Circles. Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: Angles & Arcs Class Work Circles Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: 1. Name the radii 2. Name the chord(s) 3. Name the diameter(s) 4. If AC= 7, what does TC=? 5. If

More information

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'

More information

Integrated Math II. IM2.1.2 Interpret given situations as functions in graphs, formulas, and words.

Integrated Math II. IM2.1.2 Interpret given situations as functions in graphs, formulas, and words. Standard 1: Algebra and Functions Students graph linear inequalities in two variables and quadratics. They model data with linear equations. IM2.1.1 Graph a linear inequality in two variables. IM2.1.2

More information

G.C.B.5: Arc Length 1

G.C.B.5: Arc Length 1 Regents Exam Questions G.C.B.5: Arc Length www.jmap.org Name: G.C.B.5: Arc Length The diagram below shows circle O with radii OA and OB. The measure of angle AOB is 0, and the length of a radius is inches.

More information

To construct the roof of a house, an architect must determine the measures of the support beams of the roof.

To construct the roof of a house, an architect must determine the measures of the support beams of the roof. Metric Relations Practice Name : 1 To construct the roof of a house, an architect must determine the measures of the support beams of the roof. m = 6 m m = 8 m m = 10 m What is the length of segment F?

More information

Example 1: Finding angle measures: I ll do one: We ll do one together: You try one: ML and MN are tangent to circle O. Find the value of x

Example 1: Finding angle measures: I ll do one: We ll do one together: You try one: ML and MN are tangent to circle O. Find the value of x Ch 1: Circles 1 1 Tangent Lines 1 Chords and Arcs 1 3 Inscribed Angles 1 4 Angle Measures and Segment Lengths 1 5 Circles in the coordinate plane 1 1 Tangent Lines Focused Learning Target: I will be able

More information

Similarity of Triangle

Similarity of Triangle Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree

More information

Core Mathematics 2 Coordinate Geometry

Core Mathematics 2 Coordinate Geometry Core Mathematics 2 Coordinate Geometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Coordinate Geometry 1 Coordinate geometry in the (x, y) plane Coordinate geometry of the circle

More information

10. Show that the conclusion of the. 11. Prove the above Theorem. [Th 6.4.7, p 148] 4. Prove the above Theorem. [Th 6.5.3, p152]

10. Show that the conclusion of the. 11. Prove the above Theorem. [Th 6.4.7, p 148] 4. Prove the above Theorem. [Th 6.5.3, p152] foot of the altitude of ABM from M and let A M 1 B. Prove that then MA > MB if and only if M 1 A > M 1 B. 8. If M is the midpoint of BC then AM is called a median of ABC. Consider ABC such that AB < AC.

More information

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation

More information

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below. 0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,

More information

0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?

0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below? 0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30

More information

RMT 2014 Geometry Test Solutions February 15, 2014

RMT 2014 Geometry Test Solutions February 15, 2014 RMT 014 Geometry Test Solutions February 15, 014 1. The coordinates of three vertices of a parallelogram are A(1, 1), B(, 4), and C( 5, 1). Compute the area of the parallelogram. Answer: 18 Solution: Note

More information

0811ge. Geometry Regents Exam

0811ge. Geometry Regents Exam 0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

More information

Practice Test Student Answer Document

Practice Test Student Answer Document Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

More information

Math 521B Trigonometry Assignment

Math 521B Trigonometry Assignment Math 521B Trigonometry Assignment Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the reference angle for 200 in standard position? A 100 C 20

More information

(Chapter 10) (Practical Geometry) (Class VII) Question 1: Exercise 10.1 Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only. Answer 1: To

More information

Unit 8 Circle Geometry Exploring Circle Geometry Properties. 1. Use the diagram below to answer the following questions:

Unit 8 Circle Geometry Exploring Circle Geometry Properties. 1. Use the diagram below to answer the following questions: Unit 8 Circle Geometry Exploring Circle Geometry Properties Name: 1. Use the diagram below to answer the following questions: a. BAC is a/an angle. (central/inscribed) b. BAC is subtended by the red arc.

More information

Circles Print Activity. Use the Explore It mode to answer the following questions. 1. Use the diagram below to answer the following questions:

Circles Print Activity. Use the Explore It mode to answer the following questions. 1. Use the diagram below to answer the following questions: Name: Circles Print Activity Use the Explore It mode to answer the following questions. 1. Use the diagram below to answer the following questions: a. A is a/an angle. (central/inscribed) b. A is subtended

More information

So, the measure of arc TS is 144. So, the measure of arc QTS is 248. So, the measure of arc LP is Secants, Tangents, and Angle Measures

So, the measure of arc TS is 144. So, the measure of arc QTS is 248. So, the measure of arc LP is Secants, Tangents, and Angle Measures 11-6 Secants, Tangents, Angle Measures Find each measure Assume that segments that appear to be tangent are tangent 4 1 5 So, the measure of arc QTS is 48 So, the measure of arc TS is 144 6 3 So, the measure

More information

Chapter 10. Properties of Circles

Chapter 10. Properties of Circles Chapter 10 Properties of Circles 10.1 Use Properties of Tangents Objective: Use properties of a tangent to a circle. Essential Question: how can you verify that a segment is tangent to a circle? Terminology:

More information

Core Mathematics 2 Radian Measures

Core Mathematics 2 Radian Measures Core Mathematics 2 Radian Measures Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Radian Measures 1 Radian Measures Radian measure, including use for arc length and area of sector.

More information

Geometry Unit 8 - Notes Perimeter and Area

Geometry Unit 8 - Notes Perimeter and Area Geometry Unit 8 - Notes Perimeter and Area Syllabus Objective: 8. - The student will formulate strategies for finding the perimeter or area of various geometric figures. Review terms: ) area ) perimeter

More information

SMT 2018 Geometry Test Solutions February 17, 2018

SMT 2018 Geometry Test Solutions February 17, 2018 SMT 018 Geometry Test Solutions February 17, 018 1. Consider a semi-circle with diameter AB. Let points C and D be on diameter AB such that CD forms the base of a square inscribed in the semicircle. Given

More information

Study Guide. Exploring Circles. Example: Refer to S for Exercises 1 6.

Study Guide. Exploring Circles. Example: Refer to S for Exercises 1 6. 9 1 Eploring ircles A circle is the set of all points in a plane that are a given distance from a given point in the plane called the center. Various parts of a circle are labeled in the figure at the

More information

This section will help you revise previous learning which is required in this topic.

This section will help you revise previous learning which is required in this topic. Higher Portfolio Circle Higher 10. Circle Revision Section This section will help you revise previous learning which is required in this topic. R1 I can use the distance formula to find the distance between

More information

5. Introduction to Euclid s Geometry

5. Introduction to Euclid s Geometry 5. Introduction to Euclid s Geometry Multiple Choice Questions CBSE TREND SETTER PAPER _ 0 EXERCISE 5.. If the point P lies in between M and N and C is mid-point of MP, then : (A) MC + PN = MN (B) MP +

More information

Tangent Lines Unit 10 Lesson 1 Example 1: Tell how many common tangents the circles have and draw them.

Tangent Lines Unit 10 Lesson 1 Example 1: Tell how many common tangents the circles have and draw them. Tangent Lines Unit 10 Lesson 1 EQ: How can you verify that a segment is tangent to a circle? Circle: Center: Radius: Chord: Diameter: Secant: Tangent: Tangent Lines Unit 10 Lesson 1 Example 1: Tell how

More information

Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians

Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians Class: VII Subject: Math s Topic: Properties of triangle No. of Questions: 20 Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. Greater

More information

Magnetic Fields Due to Currents

Magnetic Fields Due to Currents PHYS102 Previous Exam Problems CHAPTER 29 Magnetic Fields Due to Currents Calculating the magnetic field Forces between currents Ampere s law Solenoids 1. Two long straight wires penetrate the plane of

More information

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked

More information

Chapter-wise questions

Chapter-wise questions hapter-wise questions ircles 1. In the given figure, is circumscribing a circle. ind the length of. 3 15cm 5 2. In the given figure, is the center and. ind the radius of the circle if = 18 cm and = 3cm

More information

Section 7.2: Area of a Triangle

Section 7.2: Area of a Triangle CHAPTER 7 Trigonometric Applications to Triangles Section 7.2: Area of a Triangle Finding Areas Finding Areas Formulas for the Area of a Triangle: 600 University of Houston Department of Mathematics SECTION

More information

4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF?

4.! ABC ~ DEF,! AC = 6 ft, CB = 3 ft, AB = 7 ft, DF = 9 ft.! What is the measure of EF? Name:!!!!!!!!!!!!! Geo(2) GEOMETRY (2) REVIEW FOR FINAL EXAM #2 1. If ABC is similar to ADE, then AB AD =? AE. Which replaces the? to make the statement true? A. AC!! B. AE!! C. DE!! D. BC 2. In ABC,

More information

Lesson 6.5 Exercises, pages

Lesson 6.5 Exercises, pages Lesson 6.5 xercises, pages 498 506 3. Which strategy would you use to determine the indicated measure in each triangle? a primary trigonometric ratio the osine Law the Sine Law a) cm ) cm 37 6 cm 38 d

More information

1 What is the solution of the system of equations graphed below? y = 2x + 1

1 What is the solution of the system of equations graphed below? y = 2x + 1 1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x

More information