A b c and d are points on the circumference of a circle centre o ac is a diameter of the circle. AC and BE intersect at F.

A b c and d are points on the circumference of a circle centre o ac is a diameter of the circle The lines AB and DC are produced to meet at E. Q. Find (a) angle OCD Community Answer This answer has a 4. 2 hat O_1 2 8. (a) Find Let A and B be two different points on a circle with centre O. and C and D are points on the circumference of a circle, centre O. A. w= because x= because y= because z= because. (a) The points A, B and C lie on the circumference of a circle: centre O. D is a diameter of the circle. CD and BD are tangents to the circle. DA is a tangent to the circle. The point C is on the circumference such that angle COB= 2/3 π radians. EFH = Reason: [3] [2] 1. Angle OPT = 32° Work out the size of the angle marked x. CD=DE Angle AEC=x° Find the size of angle OED, in terms of x. Work out the values of w, x, y and z. Angle CAD=250 and angle BCD= 1320. V2015-2H Q15 D B , C and D are points on the circumference of a circle, centre O. By the tangent-secant theorem, this angle (ODB) is equal to the angle formed at the Since $$A$$A, $$B$$B, $$C$$C, and $$D$$D are points on the circumference of a circle, the quadrilateral $$ABCD$$ABC D is inscribed in the circle. Equal circles with centres O and O' touch each other at X. Give your answer in its simplest form. PO is parallel to QR and angle POQ = 48°. 7 cm"_ Work out the value of angle ABD_ 4. Corbettmaths 2023 The angle opposite the diameter is a right-angle 90°+32°+𝑥=180° 122°+𝑥=180° B, C, and D are all on the circumference of the circle and DB is the diameter. BO. To find the size of angle BCD given that angle DAB = 50 degrees, we will use properties of tangents and angles in circles. Prove that angle . Angle BOD=x° Find the size of angle BCD, in terms of x. * (b) Given that AB = 6cm and BC = 8cm, work out Q and R are points on the circumference of a circle, centre, O. BC in terms of y. 46,23,126D. Diagram NOT accurately drawn B and C are points on a circle, centre O . Arc AB = 2 arc BC and ∠AOB = 108 0. 2 In the diagram alongside, the circle with centre O is give Tangents PS and PR are drawn. www. ∵ DAE is a tangent to circle O at point A . co. are tangents to the circle. A, B, C and D are points on a circle with centre O . (a) (i) Work out the value of x. the magnitude of the following: 8. A) 27° B) 33° C) 57° D) 72° Answer by greenestamps(13039) (Show Source): The diagram shows a circle with diameter PQ. 1. DOA. Find the size of angle ABC in terms of y. 4cm. The circle below has centre C . Points C and D lie on a tangent line. On the diagram, draw a chord. Find (a) Bhat OD, (b) Bwidehat CD, (c) Cwidehat BF. Find the size of angle A. OPR = . ABC = 115^o, BAD = 70^o and AB = AD . 2. is a straight line through . PT is a tangent to the circle. O. Find an expression, in terms of x and/or y, for Find an This video explains how to solve an example on circles using properties of circles and circle theorems. AC and BE intersect at F. This and are points on the circumference of a circle, centre . Give reasons for each stage of your working A, B and D are points on the circumference of a circle, centre O. Lines ADE and BCE are straight lines, Circle Theorems Questions 1. Angle BAD = 58 Calculate the length of AC. Angle BOD= xo. A. ABO is a straight line. You V2015-2H Q15 D B , C and D are points on the circumference of a circle, centre O. Diagram not drawn to sæfe find the size of OAC- 2-30 (b) The points D, E and F lie on the circumference of another circle. Work out the size of angle DOA. 54,25,106E. (b) Given that AB = 6cm and BC = 8cm, (i) the diameter of the circle, (ii) the area of the triangle (iii) the area and circumference of the circle, leaving your The points A, B, C and D lie on the circumference of a circle, centre O. Leave blank. A, B, C and D are points on a circle. AB and AC are tangents to the circle, Angle BOC = 1300. Complete the statement. The straight lines AC and DB intersect at the point E. (ii) Give a reason for your answer www. Angle CBD=68°. C and D are points on a circle, centre O. Click here 👆 to get an answer to your question ️ The points A, B, C and D lie on the circumference of the circle, centre O. 1 In the diagram alongside, A O is the centre of circle ABEC. and Points A, B, C and D lie on the circumference of the circle. Diagram C. !A, B and C are points on the circumference of a circle with centre O. a Angle BAC = 55° Work out the size of angle ADB Give a reason for each stage of your working. [1] (2. Calculate the length of Q3 A B and D are points on the circumference of a circle centre O B O D is a diameter of the circle B C and A C are tangents to the circle Angle O C B 34 Work out the ( b ) (1. Work out the value of x. AB . A, B and C are points on the circumference of a circle with centre O. If ∠AXD = 94° and ∠CBA = 59°, find ∠DAX. Not to scale Angle CAD=28° and CD=6. a State, with a reason, which other angle is The diagram shows a circle, centre . AC is 12 cm. ∠BAC = 22° Concept used: The angle formed on circumference forming on diameter is 90° The angle at the center formed on the same arc is The points A, B and C lie on the circumference of a circle: centre O. The area of the minor segment cutoff by AC is equal to twice the area of sector BOC. To find the size of angle ∠CDE, we can use the properties of circles and angles in a triangle. 2. RT is the tangent to the circle at R Angle QRT= 560. AB = AC 12 A and B are points on a circle, centre O. AOB is a straight line. (since B B B is on the circle's circumference): ∠ B O C = 18 0 A, B, C and D are points on a circle, centre O such that AC is a diameter of the circle. ! Work out the size of the angle y. Angle OCB = 34°. Angle PBC = 100°. The line AE is a straight line through the centre of The angle at point C is angle DCB, forming a right angle with line OB (which goes directly from the center to point B), thus DCB = 90°. uk ©JustMaths 2013 Q1. Angle BCD=x° Find an expression for the size of angle BAD in terms of x. Calculate the following: 6. C is a point on the circumference such that ∠COB = θ. Angle CXB = 110° B and C are on the circumference of a circle, centre O. Angle A. (b) Calculate (i) the size of angle BAC, (li) the size of angle ABD. You A, B, C and D are points on a circle, centre O such that AC is a diameter of the circle. PR is the diameter of the circle and ST is a tangent to the circle at the point R 21 A, B, C and D are points on the circumference of a circle, centre O. If the chord AB is a diameter, then the two arcs are called 8. Angle ABC = 82° and angle ODC = 57°. −. Points A, B, C and D lie on the circumference of the circle. !B and C are points on the circumference of a circle, centre O. A, B, C and D are four points on a circle, centre O. Angle BAD 600. Using circle theorems : According to the Angles at the A,B,C and D lie on a circle, centre O. DE. A b c and d are points on the circumference of a circle centre o ac is a diameter of the circle Shown is a circle, centre O. Angle QRS = 40° and angle SOQ = 80° Prove that triangle QSR is isosceles. Angle PAD = 60° and angle BAC = 20°. Angle OCA is equal to £ radians. 5cm Not to scale A, B, C and D are points on the circumference of a circle, centre 0. Give reasons for each stage of your working. Angle DAC = 20º. Show that the size of angle OCA = 10° You must give a reason for each stage of your working. AB is the diameter of a circle, centre O. If ∠ B A D = 75 o and ∠ A C D = 25 o . . ° 5 (Total for Question 5 is 2 marks) A, B, C and D are points on the circumference of a circle. in B, C and D are points on the circumference of the circle, centre O. A and B are points on the circumference of the circle with the tangent DE going through the circle at B . (ii) Give a reason for your answer. Angle BCD = yo. DA is a tangent to the circle. T is a point such that OT = 13 cm and OT intersects circle at E. ° (Total for Question is 3 marks) Q7. Work out the size of angle BDC. By constructing various inscribed angles, we observe how they can be calculated www. Angle ATB = 2x°. Calculate the length of AC. (b) Work out the size of S and T are points on the circumference of a circle, centre O. is 90°. Work out the value of y. and D. !AC is a tangent to the circle. Diagram NOT accurately drawn . Angle CBE = 67° and angle BEC = 35° A, B, C and D are points on a circle, centre O such that AC is a diameter of the circle. You must give a reason for each stage of your working. Diagram not accurately drawn a Calculate the size of angle ABC. 4. We have the following system of equations: let $\angle{OAB} = \angle{OBA} = x$ Circle Theorems Exam Questions In the diagram below points Q and S lie on a circle centre O. 1. Angle MON is Lines JK and KI, are tangents to the circle. F. (b) A, B and C are three points on the circumference of another circle. gle TAB=58 ° gle BTA=41 ° culate the size of angle OBT u must give reasons at each stage of your working. AC and BD intersect at E. 1 hat A_1 2 8. The diagram shows a circle centre O. Calculate (a) AC^B, (b) BD^C (c) CP^D (d) AO^D A, B, C and D are points on the circumference of a circle, centre O. TA and TB are tangents to the circle. Show that . and y. Work out w. hat E_1=40 ° Determine, with reasons. CA and CB are tangents to the circle. O is the centre of the circle. (a) (i) Write down the size of angle ABC 11 In the diagram A, B, C and D are points on the circumference of a circle with centre 0. Find the value of\[\frac{DO'}{CO}\] Draw circle with the radii given below. BC^T=80∘ and CB^D=32∘. (Total 5 marks) Q7. 290 Angle A = 290 Work out the size of angle B. Angle ADO = 36° (a) Work out the size of angle AOD. AOE is a straight line. B and C are points on the circumference such that Exam Questions 2 The diagram on the right shows a circle with centre 0. AOC is a diameter of the circle. a The diagram shows a circle, centre O. Centre O. 5 rating www. and The diagram shows a circle, centre O. (a) A, B and C are points on the circumference of a circle, centre, O. Give a reason for each of your answers. C = y. [Edexcel GCSE Nov2014-2H Q17] A, B, C and D are points on the circumference of a circle, centre O. The straight-line AB is a tangent to the circle at point C. OBP is a straight line. PR is the diameter of the circle and ST is a tangent to the circle at the point R In the given figure, AB is a diameter of the circle and points C and D are on the circumference such that ∠ C A D = 30 o and ∠ C B A = 70 o what is the measure of ∠ A C D? View Solution Q 3 2^0 E B, C, D and E are points on the circumference of a circle, centre O. O is centre of the circle if ∠ A O C = 130 o then find ∠ A B C. 2] (b) angle ACE. Angle CAB=25° Angle DEC=100° Work out the size of angle DAC. B and C lie on a circle, centre O, with diameter AB. BE = 2cm and CDE = 30^{\circ} . ABE and ADF are tangents to them NOT circle. FG is a tangent at the point B The points A, B, C and D lie on the circumference of the c. 5 rating. Points P, Q, R and S lie on the circumference of the circle. are tangents to the circle B, C and D are points on the circumference of a circle, centre O. (a) (b) Write down the value of angle (i) BCD Calculate angle ABC. *B, C and D are points on the circumference of a circle, centre O. AE and AF are tangents. are points on a circle, centre . 20 BAC is a sector of a circle, centre A. x = . A, B and C are points on the circumference of the circle. DCO is a straight line. In the given diagram, A B is the diameter of the given circle with centre O. BD is a diameter of the circle and PA is a tangent to the circle at A. B and C are points on the circumference of a circle, centre O. The points A, B, C, and D in this order are concyclic. with diameter AC. Angle ABD=30° , angle CAD=50° and The points A, B, C and D lie on the circumference of the circle, centre O. !A circle with centre O, has points A, B and C on the circumference. AC is a tangent to the circle. 3 A, B and C are points on the circumference of a circle with centre AC is a diameter of the circle. Angle BAD = 70°. An example that reinforces this concept is when a circle has points A, B, C, and D on its circumference, and AC is the diameter. OCB = 34°. Identify tangent properties: Since AB and AD are tangents to the circle at points B and D, Identifying angles: We recognize that points A, B, C, and D lie on the circumference of a circle centered at O. Calculate the length of x , 4. 2 cm. marks ) 3. agram NOT rately drawn a i Write down the size of angle ABC Answer_ ii* Give a reason for your answer: _ _ 2 marks D, E and F are points on the circumference of a circle with centre 0 Angle DOF=120 ° iagram NOT urately drawn b i Work out the size of angle DEF Answer_ ii ° A, B, C and D are points on the circumference of a circle, centre O. and . BD is a diameter of the circle and PAT is the tangent to the circle at A. The diagram shows a circle, centre O. B, C and D are points on the circumference. 54,27,110F. mark) A, B, C. AĈD = x° and DÔC = yº. A, B, C and D are points on a circle with centre O. (i) Calculate angle ACB. (3 marks) _____ A, B and C are points on the circumference of a circle with centre O. Angle CDB = 22°. Sub-Topic Circle Problems (Area, Circumference, Arcs) Booklet Question Paper 1. A, B and C are points on the circumference. C . If ∠ A B D = 35 ∘ and ∠ C D B = 15 ∘, then ∠ C B D equals: B. TA is the tangent to the circle at A. BD, OCE and AF are parallel lines. If ∠ B A D = 7 5 o and ∠ A C D = 2 5 o . AC is a tangent to the circle whose centre is O. Lines ADE and BCE are straight lines, meaning they extend indefinitely in both directions. Community Answer. Edexcel GCSE Maths - Circles (H Where r is the radius and d is the diameter: Circumference of a circle = 2πr = πd Area of a circle = πr2 1 2 B and C are points on the circumference of a circle, centre O. O'D is perpendicular to AC. Write down any circle theorems that you use. on a circle, centre O. hat IC=52° and Chat In given fig. bland. Points B, C and D lie on the circumference of a circle. AD = 4. AC is a diameter and AC is parallel to ED. A, B, C and D are points on the circumference of a circle with a center O. Angle AOD=98° Work out the size of angle DBC. B and C are points on a circle, centre O. ! ! ! Shown is a circle with centre O. The sector angle is 38°. As AC = BC , we can say that ABC is an isosceles triangle. Calculate and justify your answer. S and T are points on A, B, C and D lie on the circle, centre O, with diameter AC. A, B and D are points on the circumference of a circle, centre O. Angle DAC = 23°. 1 Determine the size of Phat A, B and C are points on the circumference of the circle, centre O. BD=BC and angle DBC=62° Work out the values of w, x, y and z. AC is a diameter of the circle. b Calculate the size of angle CBD. 1120 a Angle 1120 Work out the size of angle ACB. Angle CDB = . GH is a tangent to the circle at E 650 Diagram not drawn to scale Write down the size of EFH, giving a reason for your answer. Angle DAB = 40° Angle CBE = 75° Work out the size of angle ODC. Q6. Find angle JKL. The straight line PAQ is a tangent to the circle. AEB is a tangent to the circle at E. A circle with centre O, has points A, B and C on the circumference. Find angle OPR. !AOB is a diameter of the circle. Angle OCB=34°. 5cm The circle has an area of 56. 8, O is the centre of a circle of radius 5 cm. In circle O. ACB = (90 – x)°. BD and AC intersect at E and BC is a diameter of the circle. Angle CDO = 29° Work out the size of angle AOC. Angle BOC = 130°. B, C, D and E lie on the circle, centre O. marks ) 3 In the diagram, B. A, B, C and D are four points on the circumference of a circle. BD is the diameter and AC is a chord that is perpendicular to the diameter at E. AC . Angle PAD = www. This answer has a 4. a) The chords PR and SQ of the circle intersect at T. Angle ADC=132 ° . Angle DAT=30 ° . (a) Find the size of angle ABD. BCD = 106°. AC=72cm;widehat C=63 ° and widehat B=90 ° . A and B are points on the circumference of a circle, centre O. The magnitude of ∠ B D C is 3. Diagram NOT accurately drawn In the diagram, A, B, C and D are points on the circumference of a circle, centre O. What is difference (in degrees) between the measures of ∠CAD Question: In the diagram above A,B,C and D are points on the circumference of a circle centre O. . 6% AEC and BED are straight lines. 5. B, C and D are points on the circumference of the circle, centre O. is a tangent to the circle. 46,23,106C. 0580/41/O/N/21 Q5)(b) B, C and D are points on the circle centre O. Lines ADE and BCE are straight lines, creating various angles. S and T are points on the circumference of a circle, centre O. 670 Diagram not drawn to scale Find the size of OAC The points D, E and F lie on the circumference of another circle. 4 hat C 3 8. Input note: select a reason from the list below. AC and BD intersect at P. BD is the diameter. Prove that angle ACB is 90° You must not use any circle theorems in your proof A and B are points on the circumference of a circle, centre O. AC and BD intersect at E . Click here 👆 to get an answer to your question ️ NOT TO SCALE Points A, B and C lie on a circle, centre O, with diameter AB. EF is a tangent to the circle at C. The area of the shaded region is A, B and D are points on the circumference of a circle, centre O. BC. (3) Diagram NOT accurately drawn P, Q and R are points on a circle. ∠ABD=40° and angle ∠AXB=105°I'm providing Free Online Live Maths Classes & Counsellin A , B and D are points on the circumference of a circle, centre O . C and D are two points on the circumference of the circle on either side of AB, such that ∠CAB = 42° and ∠ABD = 57°. 。 A, B, C and D are points on the circumference of a circle, centre O. Prove that angle ABC is 90° You must not use any circle theorems in your proof. Angle APO = 26! Calculate the size of angle ABP. The magnitude of ACD is Topic 4 - Circle Theorems 1 awn A, B and D are points on the circumference of a circle, centre O. A O B C (4 marks) (4 marks) 3 A O B D C A, B, C and D are points on the circumference of a circle, centre O. Chords AB and CD intersect at the point X. Write down the size of angle ABC. In the figure given A, B, C and D are four points on the circumference of a circle with centre O. could be 200 and x. In the figure given A , B , C and D are four points on the circumference of a circle with centre O. Answer: CAO = 21° Step-by-step explanation: In a circle, the angle of tangency and the inscribed angle subtended by the same arc are equal in measures . (3. The points A, B, C and D lie on a circle. A, B, C and D are points on the circumference of a circle, centre O AC is a diameter of the circle Angle DAC = 200 (a) Find the size of angle ACD (b) Find the size of angle DBC Give a reason for your answer. and R are points on the circumference of the circle, centre O. Identify the Points: We have four points A, B, C, and D on the circumference of a circle with center O. BE = 2cm and CDE = 30^o . ABE and ADF are tangents to the circle. 1 mark a State the value, in radians, of angle COA. BD is the diameter and AC is a chord that is perpendicular to the diameter at E . Work out the size of angle . 5. Angle BCD = y°. BD=BC and angle DBC=62°. 8) A, B, C and D are points on the circumference of a circle, centre O. O AC is a diameter. 18. P, Q. BC and AC are tangents to the circle. C and D are points on the circumference of a circle, centre O. Work out the size of angle DOA . You AC is a diameter. From a point P which is at a distance of 13 cm Click here👆to get an answer to your question ️ In the diagram A, B, C and D are points on the circumference of a circle. is a diameter of the circle. Angle OC'B = 340. Angle ABD=58 ° . Angle ABO = 48° (i) Find the size of angle AOB. AB is the tangent to the circle at B. C and D are on the circumference of the circle centre O. AOB is a diameter of the circle. с А. Angle ADB = 250 and angle CDB= 180. Give a reason for your answer. ADB = 57°. minutes The diagram shows a sector of a circle, centre O, radius 25 cm. Level IGCSE Subject Maths (0580) B, C, D and E are points on the circumference of a circle, centre O. In the given figure, O is the centre of the circle such that ∠AOC = 130°, then ∠ABC = 7. 8. Calculate the area of the circle. ABC is a tangent to the circle. 120 Give a reason for your answer. y. Line BD is a tangent to the circle at point B. Show that seg OD ∥ chord AC. If ∠TPQ = 70° , find the ∠TRQ. Give a reason for each stage of your working. Angle CAB = 25° Angle DEC = 100° Work out the size of angle DAC. FDE is a tangent to the circle. BD and CD are tangents. 1 2 ( a) A, B, C and D are points on the circumference of a circle, centre O. AB = AC BCE = 38' and ACD = 41'. PA is the tangent to the circle at A. (a) In the diagram below, O is the centre of the circle and A, B and C are points on the circumference. Dylan was asked to give some possible values for x. A and B are two points on the circumference of a smaller circle. could be 110, because 200 − 110 = 90" Is F ams A, B and D are points on the circumference of a circle, centre O. You must show all your working. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle. [5 marks] Write down the size of angle ABC. Find the values of u, v, w, x A, B, C and D are points on a circle, centre O. Arc AB =2 arc BC and ∠ AOB =1080. Angle PAC What is the maximum number of common points? In the given figure, O is the centre of a circle. At point C on the circle, tangent CD is drawn. PBA is a straight line. AB and AD are tangents to the circle. Give your answer correct to 3 significant figures. Total for Question is 3 marks B, C and D are points on a circle, centre O. B, C and D are points on the circumference of a circle, centre O. [1] Explain why angle . Prove that angle ABD and angle ACD are equal. E/P 8 In the diagram AB is the diameter of a circle, centre O and radius 2cm. 46,20,106B. (ii) (ii) Work out the value of x. ∵ AB is a Question: В), A E DO + с D A, B, C and D are points on the circumference of a circle, centre O. uk Circle Theorems (H) - Version 2 January 2016 4. A and D are two points on the circumference of a circle. 19. ° (Total 4 marks) 3 A, B and C are points on the circumference of a circle with centre O AC is a diameter of the circle. oct qcf' 01 = - ) sco A, B and D are points on the circumference of a circle, centre O. Angle BAD = 94° Angle ADC = 83° (i) Find the size of angle ABC. A, B, C and D are points on the circumference of a circle. Angle ABD = 58°. DOB is a straight line and angle DAC = 58°. Work out the sizes of angle ACD and ACB, giving reasons for your answers. cos θ/ 2= π (1/2− θ/ 120°) O. ADE and BCE are straight lines. BD is a diameter of the circle. Since the internal triangles you have drawn are isosceles, we can determine each of the internal angles. Diagram NOT accurately drawn A, B, C and D are points on the circumference of a circle, centre O. a) Show that y – x = 90 You must give a reason for each stage of your working. ADE and ACB are straight lines. Angle AOB = 90° angle COD= 50° and angle BCD= 1239 The line DT is a tangent to the circle at D. The shaded region, ABC, is a sector of the circle with centre C. Dwidehat AB=36°,BC=CD and EBF is a tangent to the circle at B. Points A, B, C and D lie on the circumference of a circle. CE is a diameter of the circle. Not to scale Angle CAD=28 ° and CD=6. Angle DBE = 35°. could be 110, because 200 − 110 = 90" Is 3. Angle CAB = 39° and angle ABD = 17°. leg C clic (2) 120 (2) (Total 4 marks) & ton Lots more free papers at www. is a diameter. PT and PQ are tangents to the circle from an external point P. BC . 290 D B AOB is a diameter of the circle. CA = CB. D. B, D and E are points on a circle centre O. GAF is a tangent to the circle at A. Recognize that the angle at the center of a In the diagram, A, B, C and D lie on the circle, centre O. Use the property of inscribed A, B and C are points on the circumference of a circle, centre O. Time Allowed: 64. Give a reason for each stage in your working. Let the Center of the Circle be O. The diagram shows triangle ABC and a circle, centre O. ately drawn Angle DAB=40 ° Angle CBE=75 ° Work out the size of angle ODC. (ii) PAB. In the diagram A,B,C and D are points on the circumference of a circle. Diagram NOT accurately drawn A O B P 26! Angle OAP = 90, ( angle between tangent and radius is always 90) Therefore AOB = 180 - 90 - 26 = 64 E4. DE is a tangent to the circle at E. AC is a diameter. is a straight line touching the circle at B. AD is the tangent at D to the circle In the diagram, A, B, C and D are points on the circumference of a circle, centre O. C Give reasons for each stage of your working. We know the sum of angles in triangle BCD is 180°, therefore: C D B + D CB + CB D = 180° Plugging in the known values: C D B + 90° + 58° = 180° Solving for CDB: Simplifying: C D B + 148° = 180° C D B (a) NOT TO SCALE A, B, C and D are points on the circumference of a circle centre O. AD is a diameter of the circle. A, B, C and D lie on the circle, centre O, with diameter AC. The magnitude of ∠ B D C is A, B, C and D are points on a circle, centre o AOC is a diameter of the circle. Prove that In the diagram below, A, B, C and D are points on the circumference of a circle, centre O. A, B, C. ° (4 marks) 4. A, B and C are points on the circumference. Diagram NOT accurately drawn Calculate the length of BC . ° (4) © CORBETTMATHS 2014 15. The diagram shows points A, B, C Circumference of circle = 2 Area of circle = r2 2 2 r r 4 3 3 1 2 r r2 Volume of sphere = r r h l C and D are four points on a circle, centre O. only and B. AC 17 A, B, C and D are points on the circumference of a circle, centre O. AB. 3 Ahat BE 2 8. Work out the size of angle BDC Write down any circle theorems that you use. Diagram NOT accurately drawn B and C are points on a circle, centre O. are points on the circumference of a circle, centre . 4 A O B D C ( b ) (1. 3 Circle Problems (Area, Circumference and Arcs) Question Paper. A, B and C are points on the circumference of a circle. c Explain why AC cannot be a diameter of the circle. Angle BDC = 40° In the figure, O is the centre and seg AB is the diameter. are points on the circumference of a circle, centre O is a tangent to the circle . AC is the diameter of the circle. c Diagram not drawn to scale -38) \oqo 3. OO' produced to meet a circle with centre O', at A. EDF is a tangent to the circle. A, B and C are points on the circumference of a circle, centre O. Angle BCD =128° CD = BC (a) A, B, C and D are points on the circumference of a circle, centre 0. Angle . Prove that angle ACB is 90° You must not use any circle theorems in your proof `(B) 10 sqrt2` `(C)5/sqrt2` `(D) 10sqrt 3` In Fig. [4] 5. Angle CAD = 28° and CD = 6. AB and AC are tangents to the circle. C and D are points on the circumference of the circle. Use the diagram in the diagram sheet to prove the theorem which states that ̂ =2 ̂ (6) C A B O Question Progress t n 12 1 7 16 Exam Paper Progress 34 / 80 Marks Grade For This Paper 0 A, B, C and D are four points on the circumference of a circle. ABC Question: A,B,C and D are points on the circumference of a circle, centre O. SOP is a straight line. Angle ABD=62 degrees and angle CDB= 28 degrees. PQ is a tangent to the circle at A. Angle AEB = 35°, angle ODE = 28° and angle ACD = 109°. B. These two points divide the circle into two opposite arcs. 2 In the diagram, O is the centre of the circle and A, B and C are points on the circumference of a circle. Prove that triangle OAC is congruent to triangle OBC. 128 ° _ JKL= 3 Line OR is a diameter of the circle shown below QS is a straight line that crosses the circle at P, and angle PRS is 32 ° . BE is a diameter of the circle. A, B, C & D are points on the circumference of a circl In the diagram, A B, and C are points on the circumference of the circle with centre O and radius r. A, B, C and D are points on the circumference of a circle, centre O. Explain your method. B . justmaths. 18 250 640 D AD is a diameter of a circle centre O. (c) The diameter, AC, of the circle is 13 cm. BOD is a diameter of the circle. Prove that sin θ/ 2 . Angle BOD = x°. Angle AOC=y. (a) Work out angle AOC. Angle BAD =112\deg and angle DCO =33\deg Not to scale Calculate the value of z. The points A, B, C and D lie on a circle centre O. AC. Find the values of u, v, w, x 1. are points on the circle, centre . A and B are points on a circle, centre O DBC is the tangent to the circle at B angle AOB=x show that ABC = 1/2 x give reasons for each stage in your workings. C. Find: (a) angle ACD (b) angle ADB (c) angle DAT (d) angle CAO 8 A, B, C and D are four points on the circumference of a circle. x = 1(a). He said, "y. [June 2013 Calc] *16. BD is the diameter of the circle. The chord of length 30 cm is drawn at the distance of 8 cm from the centre AB is the diameter of a circle with centre O. NOT TO SCALE A, B, C and D are points on the circumference of a circle centre O. TC is a tangent to the circle at C. x = 90. SR is a tangent to the circle at S. Question: B. (b) Work out the size of A, B, C, D and E are points on the circumference of the circle, centre O. The magnitude of ∠ B D C is A, B and C are points on the circumference of a circle, centre O. Since points A, B, C, and D lie on the To find the angle BAD given the angle ODB = 25 degrees and the tangent ED to the circle, we can use properties of circle angles. Angle CDB=22 ° , Not to scale Work out the size of angle ACB, giving a reason for your answer. Find angle CDB. B, C, D are points on the circumference of a circle with centre O . imhlsh zxzux zek cdizwar ocu bizofat oaln squhnu nbpj oifhw