Lesson 2B: Thales Theorem

Size: px
Start display at page:

Download "Lesson 2B: Thales Theorem"

Transcription

1 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 C are three distinct points on a circle with a diameter AB. Opening Exercise a. Draw any Radius in the circle 0. Label the endpoint as A. b. What do you know about radii? Home many radii a circle have? O c. Extend radius OA to be a Diameter. Label the new end point as B What do you know about Diameters? How many diameter a circle have? d. Draw another radius. This time, label the endpoint as C. What do you notice about < AOC? e. Connect A to C to create AC. This segment is called Chord f. Highlight BAC, this is called the Inscribe angle

2 Draw a diagram for each of the vocabulary words Definition Diagram Circle: The set of all points from a given point Radius: A that connects the of the circle to any point on the circle Diameter: A that passes through the and whose are on the circle Chord: A whose are on the circle Central Angle: An whose vertex is on the of the circle Inscribed Angle: An angle whose is on a circle and each of the angle intersects the circle in another. Semicircle: a circle formed by a

3 Example 1. a. Two points A and B are given. Take the index card and push it up between points A and B. b. Mark on your paper the location of the corner of the colored index card and label this as point C.(make sure the sides of the index card are always touching A and B) c. Do this again, pushing the corner of the colored index card up between A and B but at a different angle. Again, mark the location of the corner, labeling it as point D. A C B d. Continue locating points in the same manner in all directions through A and B, labeling the points as you go (create at least 8 eight points). e. What shape do the points create? f. Connect points A and B. What have you created? g. Draw in ACB. What type of angle is ACB? h. What type of triangle is ACB? THALES THEOREM: If A, B, and C are three different points on a circle with a diameter AB, then ACB is a right angle. In other words - Two chords and a diameter will always create a right triangles in a circle. Inscribed angles in a semicircle are always right angles

4 Example 2 Circle O is shown below. a. Draw diameter AB and CD of the circle. b. Connect the endpoints of the diameters c. What quadrilateral is ABCD? Explain your answer Example 3. AB is a diameter of the circle shown. The radius is cm, and AC = 7 cm. a) Find m C. b) Find AB. c) Find BC. Example 4. In the circle shown, BC is a diameter with centera. (Hint: What do you know about all the radii of a circle) Find m DAB. Find m BAE. Find m DAE.

5 Lesson 2B: Thales Theorem Classwork 1. * Give an example of each of the following for the given diagram o Diameter o Radius o Chord o Central angle o Inscribed angle o Right angle 2. **Determine the length of the radius of the circumscribed circle To the right triangle with legs 7 cm and 4 cm. Round your answer to the nearest hundredth 3. A, B, and C are three points on a circle, and angle ABC is a right angle. What is wrong with the picture below? Explain your reasoning.

6 4. ** Explain why there is something mathematically wrong with the picture at right. 5. **In the figure below AB is the diameter of the circle with radius 17 miles. miles. If BC = 30 miles, what is AC? 6. ****In the figure below, O is the center of the circle, and AD is a diameter. a. Find m AOB. b. If m AOB m COD = 3 4, what is m BOC? 7. ***Inscribe ABC in a circle of diameter 1 such that AC is a diameter. Explain why: a. sin( A) = BC. b. cos( A) = AB.

The High School Section

The High School Section 1 Viète s Relations The Problems. 1. The equation 10/07/017 The High School Section Session 1 Solutions x 5 11x 4 + 4x 3 + 55x 4x + 175 = 0 has five distinct real roots x 1, x, x 3, x 4, x 5. Find: x 1

More information

Arcs and Inscribed Angles of Circles

Arcs and Inscribed Angles of Circles Arcs and Inscribed Angles of Circles Inscribed angles have: Vertex on the circle Sides are chords (Chords AB and BC) Angle ABC is inscribed in the circle AC is the intercepted arc because it is created

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

16 circles. what goes around...

16 circles. what goes around... 16 circles. what goes around... 2 lesson 16 this is the first of two lessons dealing with circles. this lesson gives some basic definitions and some elementary theorems, the most important of which is

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

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

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

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

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

(A) 50 (B) 40 (C) 90 (D) 75. Circles. Circles <1M> 1.It is possible to draw a circle which passes through three collinear points (T/F)

(A) 50 (B) 40 (C) 90 (D) 75. Circles. Circles <1M> 1.It is possible to draw a circle which passes through three collinear points (T/F) Circles 1.It is possible to draw a circle which passes through three collinear points (T/F) 2.The perpendicular bisector of two chords intersect at centre of circle (T/F) 3.If two arcs of a circle

More information

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then

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

Copy Material. Geometry Unit 5. Circles With and Without Coordinates. Eureka Math. Eureka Math

Copy Material. Geometry Unit 5. Circles With and Without Coordinates. Eureka Math. Eureka Math Copy Material Geometry Unit 5 Circles With and Without Coordinates Eureka Math Eureka Math Lesson 1 Lesson 1: Thales Theorem Circle A is shown below. 1. Draw two diameters of the circle. 2. Identify 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

KEY STANDARDS ADDRESSED: MM2G3. Students will understand the properties of circles.

KEY STANDARDS ADDRESSED: MM2G3. Students will understand the properties of circles. KEY STANDARDS ADDRESSED:. Students will understand the properties of circles. a. Understand and use properties of chords, tangents, and secants an application of triangle similarity. b. Understand and

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

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

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

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

AREA RELATED TO CIRCLES

AREA RELATED TO CIRCLES CHAPTER 11 AREA RELATED TO CIRCLES (A) Main Concepts and Results Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle

More information

Grade 9 Geometry-Overall

Grade 9 Geometry-Overall ID : au-9-geometry-overall [1] Grade 9 Geometry-Overall For more such worksheets visit www.edugain.com Answer t he quest ions (1) A chord of a circle is equal to its radius. Find the angle subtended by

More information

Lesson 13: Angle Sum of a Triangle

Lesson 13: Angle Sum of a Triangle Lesson 13: Angle Sum of a Triangle Classwork Concept Development 1 + 2 + 3 = 4 + 5 + 6 = 7 + 8 + 9 = 180 Note that the sum of angles 7 and 9 must equal 90 because of the known right angle in the right

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

Classwork. Opening Exercises 1 2. Note: Figures not drawn to scale. 1. Determine the volume for each figure below.

Classwork. Opening Exercises 1 2. Note: Figures not drawn to scale. 1. Determine the volume for each figure below. Classwork Opening Exercises 1 2 Note: Figures not drawn to scale. 1. Determine the volume for each figure below. a. Write an expression that shows volume in terms of the area of the base,, and the height

More information

10.5 Areas of Circles and Sectors

10.5 Areas of Circles and Sectors 10.5. Areas of Circles and Sectors www.ck12.org 10.5 Areas of Circles and Sectors Learning Objectives Find the area of circles, sectors, and segments. Review Queue Find the area of the shaded region in

More information

Math 9 Unit 8: Circle Geometry Pre-Exam Practice

Math 9 Unit 8: Circle Geometry Pre-Exam Practice 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

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

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

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

Year 12 into 13 Maths Bridging Tasks

Year 12 into 13 Maths Bridging Tasks Year 1 into 13 Maths Bridging Tasks Topics covered: Surds Indices Curve sketching Linear equations Quadratics o Factorising o Completing the square Differentiation Factor theorem Circle equations Trigonometry

More information

To find the areas of circles, sectors, and segments of circles. Getting Ready! Length of Side, s. Number of Sides, n

To find the areas of circles, sectors, and segments of circles. Getting Ready! Length of Side, s. Number of Sides, n 07 Areas of Circles and Sectors Mathematics Florida Standards MAFS.912.G-C.2.5 Derive.,.the formula for the area of a sector. MP1. MP 3, MP4, MP6, MP 8 Objective To find the areas of circles, sectors,

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

Mathematical Structures for Computer Graphics Steven J. Janke John Wiley & Sons, 2015 ISBN: Exercise Answers

Mathematical Structures for Computer Graphics Steven J. Janke John Wiley & Sons, 2015 ISBN: Exercise Answers Mathematical Structures for Computer Graphics Steven J. Janke John Wiley & Sons, 2015 ISBN: 978-1-118-71219-1 Updated /17/15 Exercise Answers Chapter 1 1. Four right-handed systems: ( i, j, k), ( i, j,

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

PLC Papers. Created For:

PLC Papers. Created For: PLC Papers Created For: ed by use of accompanying mark schemes towards the rear to attain 8 out of 10 marks over time by completing Circle Theorems 1 Grade 8 Objective: Apply and prove the standard circle

More information

UNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction

UNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction Prerequisite Skills This lesson requires the use of the following skills: performing operations with fractions understanding slope, both algebraically and graphically understanding the relationship of

More information

WARM UP. Sunday, November 16, 2014

WARM UP. Sunday, November 16, 2014 WARM UP Sunday, November 16, 2014 1 2 3 4 5 6 7 8 9 10 Objectives Use properties of circles to derive the formula for sector area. Determine arc length and arc measure for given central and inscribed angle

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

Circle geometry investigation: Student worksheet

Circle geometry investigation: Student worksheet Circle geometry investigation: Student worksheet http://topdrawer.aamt.edu.au/geometric-reasoning/good-teaching/exploringcircles/explore-predict-confirm/circle-geometry-investigations About these activities

More information

Circles. II. Radius - a segment with one endpoint the center of a circle and the other endpoint on the circle.

Circles. II. Radius - a segment with one endpoint the center of a circle and the other endpoint on the circle. Circles Circles and Basic Terminology I. Circle - the set of all points in a plane that are a given distance from a given point (called the center) in the plane. Circles are named by their center. II.

More information

ieducation.com Tangents given as follows. the circle. contact. There are c) Secant:

ieducation.com  Tangents given as follows. the circle. contact. There are c) Secant: h Tangents and Secants to the Circle A Line and a circle: let us consider a circle and line say AB. There can be three possibilities given as follows. a) Non-intersecting line: The line AB and the circle

More information

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the

More information

Class X Chapter 12 Areas Related to Circles Maths

Class X Chapter 12 Areas Related to Circles Maths Exercise 12.1 Question 1: The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Radius

More information

LAMC Beginners Circle November 10, Oleg Gleizer. Warm-up

LAMC Beginners Circle November 10, Oleg Gleizer. Warm-up LAMC Beginners Circle November 10, 2013 Oleg Gleizer oleg1140@gmail.com Warm-up Problem 1 Can a power of two (a number of the form 2 n ) have all the decimal digits 0, 1,..., 9 the same number of times?

More information

LAMC Intermediate I & II March 1, Oleg Gleizer. A natural unit of measuring angles, a radian

LAMC Intermediate I & II March 1, Oleg Gleizer. A natural unit of measuring angles, a radian LAMC Intermediate I & II March 1, 2015 Oleg Gleizer prof1140g@math.ucla.edu A natural unit of measuring angles, a radian Consider an angle and a circle such that the vertex of the angle is the center of

More information

Page 1 of 15. Website: Mobile:

Page 1 of 15. Website:    Mobile: Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5

More information

What is the longest chord?.

What is the longest chord?. Section: 7-6 Topic: ircles and rcs Standard: 7 & 21 ircle Naming a ircle Name: lass: Geometry 1 Period: Date: In a plane, a circle is equidistant from a given point called the. circle is named by its.

More information

Circles and Volume. Circle Theorems. Essential Questions. Module Minute. Key Words. What To Expect. Analytical Geometry Circles and Volume

Circles and Volume. Circle Theorems. Essential Questions. Module Minute. Key Words. What To Expect. Analytical Geometry Circles and Volume Analytical Geometry Circles and Volume Circles and Volume There is something so special about a circle. It is a very efficient shape. There is no beginning, no end. Every point on the edge is the same

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

Math Day at the Beach 2018

Math Day at the Beach 2018 Multiple Choice Write your name and school and mark your answers on the answer sheet. You have 30 minutes to work on these problems. No calculator is allowed. 1. A bag has some white balls and some red

More information

CIRCLES MODULE - 3 OBJECTIVES EXPECTED BACKGROUND KNOWLEDGE. Circles. Geometry. Notes

CIRCLES MODULE - 3 OBJECTIVES EXPECTED BACKGROUND KNOWLEDGE. Circles. Geometry. Notes Circles MODULE - 3 15 CIRCLES You are already familiar with geometrical figures such as a line segment, an angle, a triangle, a quadrilateral and a circle. Common examples of a circle are a wheel, a bangle,

More information

Geometry Rules! Chapter 8 Notes

Geometry Rules! Chapter 8 Notes Geometr Rules! Chapter 8 Notes - 1 - Notes #6: The Pthagorean Theorem (Sections 8.2, 8.3) A. The Pthagorean Theorem Right Triangles: Triangles with right angle Hpotenuse: the side across from the angle

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

CBSE Board Class X Summative Assessment II Mathematics

CBSE Board Class X Summative Assessment II Mathematics CBSE Board Class X Summative Assessment II Mathematics Board Question Paper 2014 Set 2 Time: 3 hrs Max. Marks: 90 Note: Please check that this question paper contains 15 printed pages. Code number given

More information

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes Quiz #1. Wednesday, 13 September. [10 minutes] 1. Suppose you are given a line (segment) AB. Using

More information

Grade 9 Circles. Answer the questions. For more such worksheets visit

Grade 9 Circles. Answer the questions. For more such worksheets visit ID : ae-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer the questions (1) Two circles with centres O and O intersect at two points A and B. A line PQ is drawn parallel

More information

(b) Show that sin 2 =. 9 (c) Find the exact value of cos 2. (Total 6 marks)

(b) Show that sin 2 =. 9 (c) Find the exact value of cos 2. (Total 6 marks) IB SL Trig Review. In the triangle PQR, PR = 5 cm, QR = 4 cm and PQ = 6 cm. Calculate the size of PQˆ R ; the area of triangle PQR.. The following diagram shows a triangle ABC, where AĈB is 90, AB =, AC

More information

UNC Charlotte 2005 Comprehensive March 7, 2005

UNC Charlotte 2005 Comprehensive March 7, 2005 March 7, 2005 1 The numbers x and y satisfy 2 x = 15 and 15 y = 32 What is the value xy? (A) 3 (B) 4 (C) 5 (D) 6 (E) none of A, B, C or D 2 Suppose x, y, z, and w are real numbers satisfying x/y = 4/7,

More information

Mu Alpha Theta State 2007 Euclidean Circles

Mu Alpha Theta State 2007 Euclidean Circles Mu Alpha Theta State 2007 Euclidean Circles 1. Joe had a bet with Mr. Federer saying that if Federer can solve the following problem in one minute, Joe would be his slave for a whole month. The problem

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

= ( +1) BP AC = AP + (1+ )BP Proved UNIT-9 CIRCLES 1. Prove that the parallelogram circumscribing a circle is rhombus. Ans Given : ABCD is a parallelogram circumscribing a circle. To prove : - ABCD is

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

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,

More information

Fill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater

More information

CHAPTER 10 CIRCLES Introduction

CHAPTER 10 CIRCLES Introduction 168 MATHEMATICS CIRCLES CHAPTER 10 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of

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

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

The Furman University Wylie Mathematics Tournament

The Furman University Wylie Mathematics Tournament The Furman University Wylie Mathematics Tournament Senior Examination 15 February 2003 Please provide the following information: Name School Code 1. Do not open this test booklet until instructed. Instructions

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

Objectives To find the measure of an inscribed angle To find the measure of an angle formed by a tangent and a chord

Objectives To find the measure of an inscribed angle To find the measure of an angle formed by a tangent and a chord 1-3 Inscribed ngles ommon ore State Standards G-.. Identify and describe relationships among inscribed angles, radii, and chords. lso G-..3, G-..4 M 1, M 3, M 4, M 6 bjectives To find the measure of an

More information

Grade 9 Circles. Answer t he quest ions. For more such worksheets visit

Grade 9 Circles. Answer t he quest ions. For more such worksheets visit ID : th-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it

More information

Department of Mathematics

Department of Mathematics Department of Mathematics TIME: 3 Hours Setter: DS DATE: 03 August 2015 GRADE 12 PRELIM EXAMINATION MATHEMATICS: PAPER II Total marks: 150 Moderator: AM Name of student: PLEASE READ THE FOLLOWING INSTRUCTIONS

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

Name. Chapter 12: Circles

Name. Chapter 12: Circles Name Chapter 12: Circles Chapter 12 Calendar Sun Mon Tue Wed Thu Fri Sat May 13 12.1 (Friday) 14 Chapter 10/11 Assessment 15 12.2 12.1 11W Due 16 12.3 12.2 HW Due 17 12.1-123 Review 12.3 HW Due 18 12.1-123

More information

Solutions for practice questions: Chapter 7, Triangle Trigonometry If you find any errors, please let me know at

Solutions for practice questions: Chapter 7, Triangle Trigonometry If you find any errors, please let me know at Solutions for practice questions: Chapter 7, Triangle Trigonometry If you find any errors, please let me know at mailto:peggy.frisbie@polk-fl.net.. The shortest distance from the chord [AB] to the center

More information

Mathematics 5 SN TRIGONOMETRY PROBLEMS 2., which one of the following statements is TRUE?, which one of the following statements is TRUE?

Mathematics 5 SN TRIGONOMETRY PROBLEMS 2., which one of the following statements is TRUE?, which one of the following statements is TRUE? Mathematics 5 SN TRIGONOMETRY PROBLEMS 1 If x 4 which one of the following statements is TRUE? A) sin x > 0 and cos x > 0 C) sin x < 0 and cos x > 0 B) sin x > 0 and cos x < 0 D) sin x < 0 and cos x

More information

UNCC 2001 Comprehensive, Solutions

UNCC 2001 Comprehensive, Solutions UNCC 2001 Comprehensive, Solutions March 5, 2001 1 Compute the sum of the roots of x 2 5x + 6 = 0 (A) (B) 7/2 (C) 4 (D) 9/2 (E) 5 (E) The sum of the roots of the quadratic ax 2 + bx + c = 0 is b/a which,

More information

LLT Education Services

LLT Education Services 8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the

More information

11. Concentric Circles: Circles that lie in the same plane and have the same center.

11. Concentric Circles: Circles that lie in the same plane and have the same center. Circles Definitions KNOW THESE TERMS 1. Circle: The set of all coplanar points equidistant from a given point. 2. Sphere: The set of all points equidistant from a given point. 3. Radius of a circle: The

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

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

Class IX - NCERT Maths Exercise (10.1)

Class IX - NCERT Maths Exercise (10.1) Class IX - NCERT Maths Exercise (10.1) Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/interior) (ii) A point, whose distance from the centre of a circle is greater

More information

Eureka Math. Geometry, Module 5. Student File_B. Contains Exit Ticket and Assessment Materials

Eureka Math. Geometry, Module 5. Student File_B. Contains Exit Ticket and Assessment Materials A Story of Functions Eureka Math Geometry, Module 5 Student File_B Contains and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced,

More information

0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn.

0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn. 0615geo 1 Which object is formed when right triangle RST shown below is rotated around leg RS? 4 In the diagram below, congruent figures 1, 2, and 3 are drawn. 1) a pyramid with a square base 2) an isosceles

More information

11 th Philippine Mathematical Olympiad Questions, Answers, and Hints

11 th Philippine Mathematical Olympiad Questions, Answers, and Hints view.php3 (JPEG Image, 840x888 pixels) - Scaled (71%) https://mail.ateneo.net/horde/imp/view.php3?mailbox=inbox&inde... 1 of 1 11/5/2008 5:02 PM 11 th Philippine Mathematical Olympiad Questions, Answers,

More information

AREAS RELATED TO CIRCLES Introduction

AREAS RELATED TO CIRCLES Introduction AREAS RELATED TO CIRCLES 3 AREAS RELATED TO CIRCLES 1 1.1 Introduction You are already familiar with some methods of finding perimeters and areas of simple plane figures such as rectangles, squares, parallelograms,

More information

Lesson 12-13: Properties of Similarity Transformations

Lesson 12-13: Properties of Similarity Transformations Lesson 12-13: Properties of Similarity Transformations Learning Target I can define a similarity transformation as the composition of basic rigid motions and dilations. I can define two figures to be similar

More information

Class 9 Geometry-Overall

Class 9 Geometry-Overall ID : in-9-geometry-overall [1] Class 9 Geometry-Overall For more such worksheets visit www.edugain.com Answer t he quest ions (1) AB is diameter of the circle. If A and B are connected to E, circle is

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

Understand and Apply Theorems about Circles

Understand and Apply Theorems about Circles UNIT 4: CIRCLES AND VOLUME This unit investigates the properties of circles and addresses finding the volume of solids. Properties of circles are used to solve problems involving arcs, angles, sectors,

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

Circles. Riding a Ferris Wheel. Take the Wheel. Manhole Covers. Color Theory. Solar Eclipses Introduction to Circles...

Circles. Riding a Ferris Wheel. Take the Wheel. Manhole Covers. Color Theory. Solar Eclipses Introduction to Circles... Circles That s no moon. It s a picture of a solar eclipse in the making. A solar eclipse occurs when the Moon passes between the Earth and the Sun. Scientists can predict when solar eclipses will happen

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

The Theorem of Pythagoras

The Theorem of Pythagoras CONDENSED LESSON 9.1 The Theorem of Pythagoras In this lesson you will Learn about the Pythagorean Theorem, which states the relationship between the lengths of the legs and the length of the hypotenuse

More information

Trigonometry. Sin θ Cos θ Tan θ Cot θ Sec θ Cosec θ. Sin = = cos = = tan = = cosec = sec = 1. cot = sin. cos. tan

Trigonometry. Sin θ Cos θ Tan θ Cot θ Sec θ Cosec θ. Sin = = cos = = tan = = cosec = sec = 1. cot = sin. cos. tan Trigonometry Trigonometry is one of the most interesting chapters of Quantitative Aptitude section. Basically, it is a part of SSC and other bank exams syllabus. We will tell you the easy method to learn

More information

Class X Delhi Math Set-3 Section A

Class X Delhi Math Set-3 Section A Class X Delhi Math Set-3 Section A 1. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30. The distance of the car from the base of the tower (in m.) is:

More information

Geometry Facts Circles & Cyclic Quadrilaterals

Geometry Facts Circles & Cyclic Quadrilaterals Geometry Facts Circles & Cyclic Quadrilaterals Circles, chords, secants and tangents combine to give us many relationships that are useful in solving problems. Power of a Point Theorem: The simplest of

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

A. 180 B. 108 C. 360 D. 540

A. 180 B. 108 C. 360 D. 540 Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior

More information

Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior)

Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies

More information