# VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

Size: px
Start display at page:

Transcription

1 BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M: , In the adjoining figures, PQ is a tangent to a circle whose centre is C. If CP = 17 cm and the radius of the circle is 8 cm, then find the length of the tangent PQ. 2 In the adjoining figures, PA and PB are tangents from P to a circle with centre C. If. 3 In the adjoining figures, PT is a tangent to a circle whose centre is 0. If PT = 12 cm and radius of circle is 5 cm, then how far is P from O? 4 In the adjoining figures, PT is a tangent to a circle whose centre is O. If OP = 5cm and PT = 4cm, find the radius of the circle.

2 5 In the adjoining figure, PA and PB are tangents from Q to a circle with centre O. If. 6 In the adjoining figure, PA and PB are tangents from Q to a circle with centre C, If the radius of the circle is 4 cm and, then find the length of each tangent. 7 In the adjoining figure, PQ and PR are tangents from P to a circle with centre O, If. 8 In the given figure, ABC is a right-angled triangle, right angled at A, with AB =6cm and AC = 8cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle.

3 9 In the given figure find x if 10 In figure, XP and XQ are two tangents to a circle with centre O from a point X outside the circle. ARB is tangents to a circle at R. Prove that XA + AR = XB + BR. 11 In the given figure, O is the centre of the circle. Determine, if PA and PB are tangents. 12 A tangent PT is drawn parallel to a chord AB as shown in figure. Prove that APB is an isosceles triangle. 13 PAQ is a tangent to the circle with centre O at a point A as shown in figure. If, find the value of.

4 14 In the figure, AB is diameter of a circle with centre O and QC is a tangent of the circle at C. If, find. 15 The length of tangent drawn from an external point to circle are equal. Prove it. In the figure, AB and AC are two tangents to a circle with centre O from a point A outside the circle. PRQ is a tangent to circle at R. Prove that AP +PR = AQ + QR. 16 Prove that the right bisector of a chord of a circle bisects the corresponding minor arc of the circle. 17 The given figure shows two concentric circles whose common centre is O. l is a line intersecting these circles at the points A, B, C and D. Show that AB = CD. 18 In the given figure, the diameter CD of a circle with centre O is perpendicular to chord

5 AB. If AB = 12 cm and CE = 3cm, calculate the radius of the circle. 19 In the given figure, a circle with centre O is given in which a diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. Find the radius of the 20 circle. O is the centre of the circle. OAB = 20º, OCB = 55º, find BOC and AOC. 21 If a pair of opposite sides of a cyclic quadrilateral are equal, prove that the other two sides are parallel. 22 In the given figure, ABC is an isosceles triangle and O is the centre of its circumcircle. 23 Prove that AP bisects angle BPC. ABCD is a cyclic quadrilateral. If AC bisects both A and C, prove that ABC = 90º. 24 ABCD is a parallelogram. The circle through A, B and C intersects CD produced at E. Prove that AE = AD. 25 Inscribe any six-sided figure ABCDEF in a given circle. Prove that the sum of its alternate angles, i.e., A, C and E is equal to four right angles. 26 ABCD is a cyclic quadrilateral in which AB and DC when produced meet in E and EA is equal to ED. Prove that (i) AD BC (ii) EB = EC. 27 Prove that the opposite angles of a quadrilateral which is not cyclic at all cannot be supplementary. 28 In the given figure, ABC, AEG and HEC are straight lines. Prove that AHE and 29 EGC are supplementary. In figure, CD = CE = AD = AB and ACB = 58º. Find ACD and CED. Also, prove that DE AC. 30 In the given figure, PQ is a diameter. Chord SR is parallel to PQ. Given that Δ PQR = 50º, calculate: (i) RPQ (ii) STP

6 [T is a point on minor arc SP.] 31 In the given figure, two equal chords AB and CD of a circle C (O, r) when produced meet at a point E. Prove that (i) BE = DE (ii) AE = CE. 32 Prove that the line joining the midpoints of two equal chords of a circle subtends equal angles with the chords. 33 In the given figure, equal chords AB and CD of a circle C (O, r) cut at right angles at E. If M and N are the midpoints of AB and CD respectively, prove that OMEN is a square. 34 In the adjoining figure, OD is perpendicular to the chord AB of a circle with centre O. If BC is a diameter show that AC CD and AC = 2 OD. 35 Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA = QB. In the given figure, O is the centre of a circle. Prove that x + y = z. In the given figure, O is the centre of the circle. Prove that XOZ = 2( XZY + YXZ). 38 Prove that any four vertices of a regular pentagon are concyclic. 39 Prove that the sum of the angles in the four segments exterior to a cyclic quadrilateral is 40 equal to 6 right angles. gure, ABC is an isosceles triangle with AB = AC and m ABC = 50º. Find m BDC and m BEC. 41 In figure, A, B, C and D, E, F are two sets of collinear points. Prove that AD CF. 42 In figure, ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD and BC in the points E and F respectively. Prove that EF DC. 43 In figure, AB is a diameter of a circle C (O, r). Chord CD is equal to radius OC. If AC and BD when produced intersect at P, prove that ÐAPB is constant. 44 PQ and RS are two parallel chords of a circle and lines RP and SQ intersect each other at O as shown in figure. Prove that OP = OQ. 45 P is a point on the side BC of a triangle ABC such that AB = AP. Through A and C, lines are drawn parallel to BC and PA, respectively, so as to intersect at D as shown in figure. Show that ABCD is a cyclic quadrilateral. 46 Prove that the lengths of tangents drawn from an external point to a circle are equal.

7 Use the above result in the following : A circle is inscribed in a ΔABC, touching AB, BC and AC at P, Q and R respectively, as shown in fig. If AB = 10 cm, AR = 7 cm and RC = 5 cm, then find the length of BC. (2010) 47 In fig. a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm 2, then find the lengths of sides AB and AC. (2011) 48 In fig. PQ and PR are two tangents from an external point P to the circle with centre O. If, prove that OP = 2PQ. (2010) 49 In fig. two tangents PQ and PR are drawn to a circle with centre O from an external point P. Prove that. OR Prove that the parallelogram circumscribing a circle is a rhombus. (2010) 50 Prove that the lengths of tangents drawn from an external point to a circle are equal. (2010) 51 In fig, if AB = AC, prove that BE = EC. 52 In fig, OP is equal to diameter of the circle. Prove that ABP is an equilateral triangle. 53 In fig, AB is a chord of length 9.6 cm, of a circle with centre O and radius 6 cm. The tangents at A and B intersect at P. Find the length of PA. 54 In fig, a circle is inscribed in a quadrilateral ABCD in which. If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius (r) of the circle. 55 A circle is inscribed in a ΔABC, touching AB, BC and AC at P, Q and R respectively, as shown in Fig. If AB = 10 cm, AR = 7 cm and RC = 5 cm, then find the length of BC. 56 From an external point P, two tangents PA and PB are drawn to a circle with centre O as shown in fig. Show that OP is the perpendicular bisector of AB. 57 In fig, PA and PB are two tangents drawn to a circle with centre O, from an external point

8 P such that PA = 5 cm and. Find the length of chord AB. 58 Two tangents TP and TQ are drawn from an external point T to a circle with centre at O, as shown in fig. If they are inclined to each other at an angle of 100º then what is the value of. 59 In fig, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD. 60 In fig, the incircle of ΔABC touches the sides BC, CA and AB at D, E and F respectively. If AB = AC, prove that BD = CD. 61 In fig, ABC is a right-angled triangle with AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle. 62 In fig, if find. 63 Using the above: Prove that PP = QQ in fig. 64 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Using the above, do the following: (i) In fig, O is the centre of the two concentric circles. AB is a chord of the larger circle touching the smaller circle at C. Prove that AC = BC.

### 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

### 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

= ( +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

### Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths

Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is

### 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

### 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.

### (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

### 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

### SSC CGL Tier 1 and Tier 2 Program

Gurudwara Road Model Town, Hisar 9729327755 www.ssccglpinnacle.com SSC CGL Tier 1 and Tier 2 Program -------------------------------------------------------------------------------------------------------------------

### Udaan School Of Mathematics Class X Chapter 10 Circles Maths

Exercise 10.1 1. Fill in the blanks (i) The common point of tangent and the circle is called point of contact. (ii) A circle may have two parallel tangents. (iii) A tangent to a circle intersects it in

### 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

### (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

### 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 =,

### 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

### Question 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =

Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain

### 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

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

### Question Bank Tangent Properties of a Circle

Question Bank Tangent Properties of a Circle 1. In quadrilateral ABCD, D = 90, BC = 38 cm and DC = 5 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 7 cm. Find

### 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

### 1. Prove that the parallelogram circumscribing a circle is rhombus.

UNIT-9 1. Prve that the parallelgram circumscribing a circle is rhmbus. Ans Given : ABCD is a parallelgram circumscribing a circle. T prve : - ABCD is a rhmbus r ABBCCDDA Prf: Since the length f tangents

### 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

### It is known that the length of the tangents drawn from an external point to a circle is equal.

CBSE -MATHS-SET 1-2014 Q1. The first three terms of an AP are 3y-1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)

### QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)

QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents

### 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

### 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

### 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

### 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

### MOCKTIME.COM ONLINE TEST SERIES CORRESPONDENCE COURSE

GEOMETRY TRIANGLES AND THEIR PROPERTIES A triangle is a figure enclosed by three sides. In the figure given below, ABC is a triangle with sides AB, BC, and CA measuring c, a, and b units, respectively.

### AREAS OF PARALLELOGRAMS AND TRIANGLES

AREAS OF PARALLELOGRAMS AND TRIANGLES Main Concepts and Results: The area of a closed plane figure is the measure of the region inside the figure: Fig.1 The shaded parts (Fig.1) represent the regions whose

### 1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM.

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 2. Let ABCD be a cyclic quadrilateral inscribed in a circle

### Chapter 3. - parts of a circle.

Chapter 3 - parts of a circle. 3.1 properties of circles. - area of a sector of a circle. the area of the smaller sector can be found by the following formula: A = qº 360º pr2, given q in degrees, or!

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

### ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.

Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line

### 6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.

6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has

### EXERCISE 10.1 EXERCISE 10.2

NCERT Class 9 Solved Questions for Chapter: Circle 10 NCERT 10 Class CIRCLES 9 Solved Questions for Chapter: Circle EXERCISE 10.1 Q.1. Fill in the blanks : (i) The centre of a circle lies in of the circle.

### INVERSION IN THE PLANE BERKELEY MATH CIRCLE

INVERSION IN THE PLANE BERKELEY MATH CIRCLE ZVEZDELINA STANKOVA MILLS COLLEGE/UC BERKELEY SEPTEMBER 26TH 2004 Contents 1. Definition of Inversion in the Plane 1 Properties of Inversion 2 Problems 2 2.

### 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,

### 3. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is:

Solved Paper 2 Class 9 th, Mathematics, SA 2 Time: 3hours Max. Marks 90 General Instructions 1. All questions are compulsory. 2. Draw neat labeled diagram wherever necessary to explain your answer. 3.

### 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

### 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

### RMT 2013 Geometry Test Solutions February 2, = 51.

RMT 0 Geometry Test Solutions February, 0. Answer: 5 Solution: Let m A = x and m B = y. Note that we have two pairs of isosceles triangles, so m A = m ACD and m B = m BCD. Since m ACD + m BCD = m ACB,

### 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:

### = 0 1 (3 4 ) 1 (4 4) + 1 (4 3) = = + 1 = 0 = 1 = ± 1 ]

STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. If the lines x + y + = 0 ; x + y + = 0 and x + y + = 0, where + =, are concurrent then (A) =, = (B) =, = ± (C) =, = ± (D*) = ±, = [Sol. Lines are x + y + = 0

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

### 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

2D VECTORS Question 1 (**) Relative to a fixed origin O, the point A has coordinates ( 2, 3). The point B is such so that AB = 3i 7j, where i and j are mutually perpendicular unit vectors lying on the

### CBSE X Mathematics 2012 Solution (SET 1) Section B

CBSE X Mathematics 01 Solution (SET 1) Section B Q11. Find the value(s) of k so that the quadratic equation x kx + k = 0 has equal roots. Given equation is x kx k 0 For the given equation to have equal

### Circle and Cyclic Quadrilaterals. MARIUS GHERGU School of Mathematics and Statistics University College Dublin

Circle and Cyclic Quadrilaterals MARIUS GHERGU School of Mathematics and Statistics University College Dublin 3 Basic Facts About Circles A central angle is an angle whose vertex is at the center of the

### 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

### chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?

chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "

### Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer: Let the common ratio between

### Class IX Chapter 8 Quadrilaterals Maths

1 Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Let the common ratio between the angles

### TRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions

CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)

### 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

### 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

### 8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

8. Quadrilaterals Q 1 Name a quadrilateral whose each pair of opposite sides is equal. Mark (1) Q 2 What is the sum of two consecutive angles in a parallelogram? Mark (1) Q 3 The angles of quadrilateral

### Maharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40

Maharashtra Board Class X Mathematics - Geometry Board Paper 04 Solution Time: hours Total Marks: 40 Note: - () All questions are compulsory. () Use of calculator is not allowed.. i. Ratio of the areas

### 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

### 1 / 24

CBSE-XII-017 EXAMINATION CBSE-X-01 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instuctions : 1. All questions are compulsory.. The question paper consists of 34 questions

### Circles. Exercise 9.1

9 uestion. Exercise 9. How many tangents can a circle have? Solution For every point of a circle, we can draw a tangent. Therefore, infinite tangents can be drawn. uestion. Fill in the blanks. (i) tangent

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

### 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

### Geometry: Introduction, Circle Geometry (Grade 12)

OpenStax-CNX module: m39327 1 Geometry: Introduction, Circle Geometry (Grade 12) Free High School Science Texts Project This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution

### Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?

Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel

### POINT. Preface. The concept of Point is very important for the study of coordinate

POINT Preface The concept of Point is ver important for the stud of coordinate geometr. This chapter deals with various forms of representing a Point and several associated properties. The concept of coordinates

### Collinearity/Concurrence

Collinearity/Concurrence Ray Li (rayyli@stanford.edu) June 29, 2017 1 Introduction/Facts you should know 1. (Cevian Triangle) Let ABC be a triangle and P be a point. Let lines AP, BP, CP meet lines BC,

### Answer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK-12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4.

9.1 Parts of Circles 1. diameter 2. secant 3. chord 4. point of tangency 5. common external tangent 6. common internal tangent 7. the center 8. radius 9. chord 10. The diameter is the longest chord in

### COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use

COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE I. Length of a Line Segment: The distance between two points A ( x1, 1 ) B ( x, ) is given b A B = ( x x1) ( 1) To find the length of a line segment joining

### Concurrency and Collinearity

Concurrency and Collinearity Victoria Krakovna vkrakovna@gmail.com 1 Elementary Tools Here are some tips for concurrency and collinearity questions: 1. You can often restate a concurrency question as a

### 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

### Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.

Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?

### Circles, Mixed Exercise 6

Circles, Mixed Exercise 6 a QR is the diameter of the circle so the centre, C, is the midpoint of QR ( 5) 0 Midpoint = +, + = (, 6) C(, 6) b Radius = of diameter = of QR = of ( x x ) + ( y y ) = of ( 5

### Part (1) Second : Trigonometry. Tan

Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,

### SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)

1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x

### KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)

### Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD?

Class IX - NCERT Maths Exercise (7.1) Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Solution 1: In ABC and ABD,

### 1. Observe and Explore

1 2 3 1. Observe and Explore 4 Circle Module - 13 13-.1 Introduction : Study of circle play very important role in the study of geometry as well as in real life. Path traced by satellite, preparing wheels

### 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)

### 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

### Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1

Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1 1 Triangles: Basics This section will cover all the basic properties you need to know about triangles and the important points of a triangle.

### Class IX Chapter 7 Triangles Maths

Class IX Chapter 7 Triangles Maths 1: Exercise 7.1 Question In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD,

### 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

### CBSE Sample Paper-03 (Unsolved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90

CBSE Sample Paper-3 (Unsolved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX Time allowed: 3 hours Maximum Marks: 9 General Instructions: a) All questions are compulsory. b) The question paper consists

### Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or

STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R

### Full Question Paper Maths, X Class

Full Question Paper Maths, X Class Time: 3 Hrs MM: 80 Instructions: 1. All questions are compulsory. 2. The questions paper consists of 34 questions divided into four sections A,B,C and D. Section A comprises

### Class IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).

Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD, AC = AD (Given) CAB = DAB (AB bisects

### Geometry Honors Review for Midterm Exam

Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers

First day. 8 grade 8.1. Let ABCD be a cyclic quadrilateral with AB = = BC and AD = CD. ApointM lies on the minor arc CD of its circumcircle. The lines BM and CD meet at point P, thelinesam and BD meet

### Berkeley Math Circle, May

Berkeley Math Circle, May 1-7 2000 COMPLEX NUMBERS IN GEOMETRY ZVEZDELINA STANKOVA FRENKEL, MILLS COLLEGE 1. Let O be a point in the plane of ABC. Points A 1, B 1, C 1 are the images of A, B, C under symmetry

### 9. Areas of Parallelograms and Triangles

9. Areas of Parallelograms and Triangles Q 1 State true or false : A diagonal of a parallelogram divides it into two parts of equal areas. Mark (1) Q 2 State true or false: Parallelograms on the same base

### 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

### SUMMATIVE ASSESSMENT II SAMPLE PAPER I MATHEMATICS

SUMMATIVE ASSESSMENT II SAMPLE PAPER I MATHEMATICS Class: IX Time: 3-3 ½ hours M.Marks:80 General Instructions: 1. All questions are compulsory 2. The question paper consists of 34 questions divided into

### TOPPER SAMPLE PAPER 3 Summative Assessment-II MATHEMATICS CLASS X

TOPPER SAMPLE PAPER 3 Summative Assessment-II MATHEMATICS CLASS X M.M: 80 TIME : 3-3 2 Hrs. GENERAL INSTRUCTIONS :. All questions are compulsory. 2. The question paper consists of 34 questions divided

### (b) the equation of the perpendicular bisector of AB. [3]

HORIZON EDUCATION SINGAPORE Additional Mathematics Practice Questions: Coordinate Geometr 1 Set 1 1 In the figure, ABCD is a rhombus with coordinates A(2, 9) and C(8, 1). The diagonals AC and BD cut at

### TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad

TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad J-Mathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =

### 1 / 23

CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar

### CHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles

CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a