Upload File

circle theorems - maths · 1. t is a point on a circle, centre o. q is a point such that angle qto...

  • Home
  • Documents
  • Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the
12
Instructions • Use black ink or ball-point pen. • Fill in the boxes at the top of this page with your name. • Answer all questions. • Answer the questions in the spaces provided – there may be more space than you need. • Show all your working out Information • The total mark for this paper is 40. • The marks for each question are shown in brackets. – use this as a guide as to how much time to spend on each question. • Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed Advice • Read each question carefully before you start to answer it • Attempt every question • Check your answers if you have time at the end GCSE (9-1) Grade 6 Circle Theorems Name:…………………………………………………….. Total Marks:……………………………………………

Upload: others

Post on 09-Oct-2020

13 views

Category:

Documents


0 download

Report

TRANSCRIPT

Page 1: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

Instructions

• Use black ink or ball-point pen. • Fill in the boxes at the top of this page with your name. • Answer all questions. • Answer the questions in the spaces provided

– there may be more space than you need. • Show all your working out

Information

• The total mark for this paper is 40. • The marks for each question are shown in brackets.

– use this as a guide as to how much time to spend on each question.

• Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed

Advice

• Read each question carefully before you start to answer it • Attempt every question • Check your answers if you have time at the end

GCSE (9-1) Grade 6 Circle Theorems

Name:…………………………………………………….. Total Marks:……………………………………………

Page 2: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

1.

T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the circle. Work out the size of angle OPT.

...........................................................°

(Total 3 marks) ___________________________________________________________________________

Page 3: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

2.

A, B, C and D are points on a circle, centre O. AE is a tangent to the circle. Angle ADC = 68° (a) (i) Find the size of angle ABC.

........................................................... ° (ii) Give a reason for your answer.

................................................................................................................................................

(2) (b) (i) Find the size of angle AOC.

........................................................... ° (ii) Give a reason for your answer. ...............................................................................................................................................

(2)

Page 4: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

(c) Find the size of angle CAE.

........................................................... °

(1) (Total 5 marks)

___________________________________________________________________________

3.

D, E, F, G and H are points on a circle. Angle EGH = 67° (a) Find the size of angle EFH.

...........................................................°

(1) (b) Give a reason for your answer. ................................................................................................................................................ ................................................................................................................................................

(2) (Total 3 marks)

___________________________________________________________________________

Page 5: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

4.

A, B, C and D are points on a circle, centre O. Angle ADB = 57°. Angle BCD = 106°. (a) (i) Calculate the size of angle AOB.

...........................................................° (ii) Give a reason for your answer. ............................................................................................................................................... ................................................................................................................................................

(2)

(b) Calculate the size of angle BAD.

...........................................................°

(1)

(Total 3 marks) ___________________________________________________________________________

Page 6: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

5.

A, B, C and D are four points on a circle, centre O. AD is a diameter of the circle. Angle BAD = 58° (a) Calculate the size of angle ADB.

...........................................................°

(2)

(b) (i) Calculate the size of angle BCD.

...........................................................°

(ii) Give a reason for your answer. …............................................................................................................................................

...............................................................................................................................................

(2) (Total 4 marks)

___________________________________________________________________________

Page 7: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

*6.

T and R are two points on a circle centre O. PT and PR are the tangents to the circle from P.

Angle TPO = 20°. Work out the size of angle TOR. You must give reasons for each stage of your working.

(Total 4 marks) ___________________________________________________________________________

Page 8: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

*7.

A and B are points on the circumference of a circle, centre O. AT is a tangent to the circle. Angle TAB = 58°. Angle BTA = 41°. Calculate the size of angle OBT. You must give reasons at each stage of your working.

(Total 5 marks) ___________________________________________________________________________

Page 9: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

8.

A, B and D are points on the circumference of a circle, centre O. BOD is a diameter of the circle. BC and AC are tangents to the circle. Angle OCB = 34°. Work out the size of angle DOA.

…. .................................................................................................................................................

(Total 3 marks) ___________________________________________________________________________

Page 10: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

9.

S and T are points on the circumference of a circle, centre O. PT and PS are tangents. Angle TPO = 24°. Work out the size of angle SOT.

. . . . . . . . . . . . . . . . . . . . . .°

(Total 3 marks) ___________________________________________________________________________

Page 11: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

10.

B, C and D are points on the circumference of a circle, centre O. ABE and ADF are tangents to the circle. Angle DAB = 40° Angle CBE = 75° Work out the size of angle ODC.

...........................................................°

(Total 3 marks) ___________________________________________________________________________

Page 12: Circle Theorems - Maths · 1. T is a point on a circle, centre O. Q is a point such that angle QTO = 58° P is the point such that OP is parallel to QT and PT is a tangent to the

www.naikermaths.com

11.

A, B, C and D are points on the circumference of a circle, centre O. AC is a diameter of the circle. AC and BD intersect at E. Angle CAB = 25° Angle DEC = 100° Work out the size of angle DAC. You must show all your working.

........................................................... ° (Total 4 marks)

___________________________________________________________________________ TOTAL FOR PAPER: 40 MARKS


Home - Warren County Public Schools...12.1 Tangent Lines A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. B The point where

pdf.Std VI - wssbxr.in · The fixed point is called the centre of the circle, and the constant distance is Imown as the radius of the circle. Let O be the centre of a circle of radius

"THIRD CIRCLE" thriller power point

Circle Basics Central Angles. Definition - Circle A circle is the collection of all points in a plane equidistant from a given point called the center

© T Madas. What is an epicycloid? Imagine a circle rolling on the outside of another circle. Pick a fixed point on the rolling circle and follow its path

DDA & BRESENHAMS, Circle (Mid Point Approch)

Circle Circle Area of a Circle Area = π r 2. Circle Circle- is a line forming a closed loop, and every point on which is fixed distance from a center

Equations of Circles. Vocab Review: Circle The set of all points a fixed distance r from a point (h, k), where r is the radius of the circle and the point

6.1 Circles and Circumference - Big Ideas Math 6/06/… · a point called the center. circle center The radius is the distance from the center to any point on the circle. The diameter

Concept Summary Belton High School Physics. Circular Motion Terms The point or line that is the center of the circle is the axis of rotation.The point

The Mohr circle for any point in the Engineering 2017_Set-1... · The Mohr circle for any point in the soil sample would be A. a circle of radius and center at the origin B. a circle

The Point Within the Circle 1

Tangents and Secants t ircle - Sakshi Education · a) There is no tangent to a circle through a point which lies inside the circle. b) There is only one tangent to a circle passing

Tangents- Definition Geometric Constructions A line is a tangent to a circle if it touches the circle at only one point

Mohr’s Circle · PDF fileDerivation of Mohr’s Circle ... Draw a line from point A to point B, a diameter of the circle passing through point c (center of circle). Points A and

Section 9.5 Tangent - Ken Jones · 2019. 4. 11. · Tangents A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of

51 - NPTEL · 2017. 8. 4. · A Pole is a unique point located on the circumference of Mohr’s circle. The point of intersection of Mohr’sstress circle and line drawn through the

Point Within the Circle

Section 10.1 Circles. 10.1 Notes What is a CIRCLE? A CIRCLE is the set of all points in a plane equidistant from a given point

Miami Circle at Brickell Point - Mission San Luisinfo.flheritage.com/miami-circle/More/Landmark_Nomination.pdf · all of coastal Miami. The bedrock underlying the site is Miami Oolite,

 · A circle is a set of points (a locus) which are equidistant from a fixed point called the 'centre'. The distance from the centre to any point on the circle is called the 'radius

9 Point Circle

District CIRCLE NAME/SALES POINT

Tangents to a Circle: The angle between a tangent and the radius drawn to the point of contact is 900. Z = 900 From any point outside a circle just two tangents to the circle may

Circles > Formulas Assignment is Due. Center Circle: A circle is the set of all points in a plane that are equidistant from a given point called the center

Circles. Parts of a Circle Circle 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

T… · 12.1 Tangent Lines A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. B The point where a circle and a tangent intersect

Table of Contentsmk0tqcsheendm9hfmnd0.kinstacdn.com/wp...3) Circle-radius: click, left-click to choose a start point for a circle; draw the circle to an end point, release the mouse,

Thales and the Nine-point Conicmat.msgsu.edu.tr/.../nine-point-conic-2018-03-14.pdf · these nine points lie on a circle, called the nine-point circle or Euler circle of the triangle

Circles Chapter 9. Tangent Lines (9-1) A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The

scan conversion of point , line and circle

8.3Circle Challenges · the circle? 2. Sapana’schallenge: The points (0, 5) and (0,-5) are the endpoints of the diameter of a circle. The point (3, y) is on the circle. What is

Circles. A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. circle A, or A

Geometrical Constructions 1 · Inscribed circle or incircle touches is tangent to the triangle’s three sides. ... nine-point circle (or Feuerbach’scircle). (HF = FO) CIRCLES AND

Application of Nine Point Circle Theorem · In mathematics geometry, a nine-point circle is a circle that can be constructed from ... 3.4.2 Irregular Polygons Chapter 4 - Results