In the diagram ab is an arc of a circle with centre o. The tangent at A and the tangent at 8 meet at the point C.

In the diagram ab is an arc of a circle with centre o Chord [AB] has length L and Awidehat OB= θ radians. (i) Find the perimeter of the shaded region. c Find the area of the shaded region. Calculate i Length of arcADC [1 ii Length of CB iii Perimeter of shaded region The diagram shows triangle ABC in which AB is [perpendicular to BC . the length of the arc AB is 4cm . The diagram shows a sector OACB of a circle with centre The point C is the midpoint of the arc AB. [2] ii Given that the minor arc AB has length 12 cm, find the value of r and of θ. (2) (b) Find the area of the sector OAB. Work out the length of arc . Math Mode 6 a) The following diagram shows part of a circle with centre O and radius 4 cm. The diagram shows a sector AOB of a circle with centre O and radius scm. Calculate the area of sector . The point C lies on the circle with centre O. In the given figure, AC is the diameter of circle, centre O. The length of the minor arc AB is 28cm. a Find the area of R, giving your answer to 2 decimal places. [1] b State the perimeter of the shaded motif in terms of π and r. [Maximum mark: 6] The following diagram shows a circle with centre O and radius r. It is given that the perimeter of the sector is 20cm. Answer to р 8 10. The diagram shows the figure ABC. [2] b Find the area of the shaded region. Angle AOB= θ radians. The diagram shows a circle with centre O and radius r cm. a) The diagram shows a circle with centre O and radius 42 cm. 4 marks rcm The shaded segment T is enclosed by the straight line AB and the arc AB. The following diagram shows a circle of centre O, and radius 15 cm. Area of arc = × Radius of circle. Angle AOB is θ radians. a Calculate, in radians, the size of the acute angle AOB. Diagram NOT accurately drawn Angle AOB=96° (a) Work out the size of angle ACB. (In the above figure, OBC is a sector). 2cm^2. O 2 y= x−3 −1+ x−3 The diagram shows part of the curve for the case when k= 1. The point C lies on the circle with centre 0. (i) Show that angle BAO is 0. The area of the shaded sector AOB is 12 cm2 and the length of the arc AB is 8 cm. ED=22cm and DC=18cm Calculate (a) the perimeter of the cross-section, (b) the area of the cross-section, (c) the volume of the box, (d) the total surface area of the box Mar 26, 2019 · Area of arc = × Radius of circle. Hence, calculate (i) the length of the arc APB. 8cm3 and height 3. The arc also subtends the angle APB, called an angle at the circumference subtended by the arc AB. [2] (ii) Find the perimeter of the shaded region. The following diagram shows a circle with centre O and radius 3. com Edexcel 1 . Explanation: Radius 9 cm. The centre of the smaller circle is O and lies on the circumference of the larger circle. The diagram above shows the sector OAB of a circle with centre O, radius 9 cm and angle 0. The line overline AB;; u tangent to the circle at B and A is the mid-point of QX. Show that arc APB has length 6π−3θ. (1) ∠ AOB (2)∠ ACB In the diagram, ABC is an arc of the circle centre O, radius 5 and angle AOC is 1. Dec 18, 2020 · In the diagram, AB is an arc of a circle with centre O and radius 4 cm. The arc ACB subtends an angle of 2 radians at the centre O. 73 cm, correct to 3 significant figures. Angle AOB = 80 o and angle ACE = 10 o. (a) Show that the size of ∠ AOB is exactly 1. The arc DC, with centre O, meets OA at C. O rad In the diagram, AB is an arc of a circle, centre O and radius r cm, and angle AOB point X lies on 0B and AX is perpendicular to OB. (5 marks) In the diagram, AOB is a quarter circle with centre O and radius r. Find the area of the shaded region. (a) Find the length of the arc AB. (5 marks) (Give your answer to 4 significant figures) ii) Find the area of the sector AOB (shaded area). Question 49 Circular Measure The diagram shows a major arc AB of a circle with centre O and radius 6 cm. Draw a circle with centre O and radius $$4\, cm. An equilateral triangle BCO adjoins the sector. (1) ∠ AOB (2)∠ ACB The diagram shows two arcs, A and B. (5 marks) ii) Find the area of the sector AOB (shaded area). Angle A O B is α radians. [4] c Find the perimeter of the shaded region. b Hence, find the exact area of the non-shaded region. CD and BE are parallel. (i) Show that the angle 4OB is 1. Find the area of the shaded region, in terms of θ . Angle AOB is θ radians. 6 cm2. (ii)the perimeter of the shaded region. ) The diagram below shows a circle, centre O, with a radius 12 cm. OAB is a sector of a circle, centre O. the angle between the radii OA and OB is θ radians. ∠BAO = 36° ∠BCO = 48° O B X A 6 cm 1 3 p = 1 3 In the diagram, AB is an arc of a circle, centre O and radius 6cm, and angle AOB πradians. 6 , find the area of the shaded region. The diagram shows a sector of a circle of radius 7 cm. The shaded region is bounded by two arcs. Calculate : Angle BCD In the diagram, arc AB is part of a circle with centre 0 and radius 8cm. 85 radian. Use angle θ in radians. The length of the arc AB is 8 cm. 45r. and radius 15 cm. Angle AOB=θ radians. B 08 Let 0= AOB. The angle 4OB is θ radians. ii For the case where a = 1 īt, find Aug 11, 2023 · AB and BC are two chords of a circle with centre O. 2 , find the area of the shaded region. (i) Show that the area, A cm2, of the shaded region AXB is given by — sin cos B). The diagram shows a sector OAB of a circle, centre O and radius 7. The cross-section of the box is shown in Diagram 2, with all the right-angles marked. [1] (b) Find the perimeter of the shaded region [3] Dec 11, 2021 · Co ordinate geometry of the major arc AB. radius 12cm and angle 1. Point A and point C are connected to the centre O. [4] 2 9cm O P Q T m In the diagram, the circle has centre O and radius 5cm. AD and CE are diameters of th and DE is a straight line. 70 radians correct to 2 decimal places. (a) In the diagram below, O is the centre of the circle and A, B and C are points on the circumference. 4 12 cm rad A The diagram shows a circle with centre O and a chord AB. Show that arc APB has length 6 π -3 θ . Upload Image. The [3] (ii) In the case where r = 12 and 9 answer in tenns of v/ 3 and lt. The diagram shows a circle with centre O. [4] ii For the case where r=5cm and θ =0. (ii) Find the area of the shaded region. It is given that the length of the arc AB is 9. Express each of the following in terms of r, π and sqrt(3) (i) the perimeter of the shaded region, (iii)the area of the shaded region. Find an expression in terms of α for the perimeter of the shaded region ABDC. 4. (ii) the area of the shaded region 10. 3 ii 31. (Give your answers to 2 decimal places) 110° Calculate the length of arc AB. a. For the case where α = 1 6 π, find the area of the shaded region A B D C, giving your answer in the form k π, where k is a constant to be Question: In the diagram, AOB is a quarter circle with centre O and radius r. the mid-point of AB, and OX is perpendicular to AB The shaded region is bounded by the chord AB and by the are of a circle with centre X and radius XA [3] Show that angle AXB is 2. Click here 👆 to get an answer to your question ️ In the diagram, AB is an arc of a circle with centre O : m. (b) Find the perimeter of the shaded region. The region R is bounded by the arc AB and the lines AC and CB. [2] (b) Find the perimeter of the shaded shape. Calculate In the diagram, A B is an arc of a circle with centre O and radius 4 cm. Chord [AB] has length L and AOB=θ radians. 4 cm. The line AC is a tangent to the circle with centre O, and OBC is a straight line. In the diagram, O is the centre of the circle ACBQ of radius 20 cm. AB is an arc of a circle, centre O, radius 12 cm. (0) Show that the area, A cm2, of the shaded region AXB is given by As r2(?-sin ? cos ?). Find the area of the sector in terms of r, giving your answer in its simplest form. (3 marks) a= frac // b= 6. Hint: The basic concepts involved in this question are: Sector: A sector is a region enclosed between two radii and an arc in a circle. Diagram not drawn to scale A rope is used to mark the boundary of the whole landing area. Points A, P and B lie on the circumference of the circle. Volume of cos alpha = 1/3 π r'h The diagram also shows a hollow cone with vertex O. The length of arc PQ is 7 cm. Angle COD = 1. PointP lies on ABand OP is an arc of a circle with centreA. O A. The point D lies on AB, and DC is an arc of a circle with centre B. Arc AB subtends an angle 0 radians at O. i Given that the angle θ is obtuse, find θ. (i) Show that the radius of the arc CED is 3. [1] The diagram shows an arc, AB, of a circle, centre O. CHAPTER 11 TRIGONOMETRY 11 In the diagram, OAB is a sector of a circle with centre 0 and radians. a) find the value of θ. Show that the area enclosed by the two arcs is equal to 25 (√ 3 − π 6) c m 2 : The diagram shows a circle with centre O and radius r. The sector angle is 72º. The length of the arc AB is 6 pie cm. The radius of the circle is 8. Given that angle = 55° work out the area of the circle. 4 radians and angle AOC=0. 5 cm. Find (a) the length of the arc ACB; (b) the area of the shaded region. The points A and B lie on the circumference of the circle. (2 marks) The area of the minor sector AOB is R_1cm^2 and the area of the shaded major sector is R_2cm^2. 2)An arc of a circle In the diagram, AOB is a quarter circle with centre O and radius r. Arc CD is part of a circle with centre O and radius 10cm. The angle AOB is θ radians. 8cm^2. Angle AOB is 2. Calculate i Length of arcADC [1 ii Length of CB iii Perimeter of shaded region The box is a prism of length 40 cm. 7297 , correct to 4 decimal places. 9 radians. A 2 (a) Calculate the area of the segment BDCP (b) Calculate the area of the shaded region BECD. Angle AOB is α radians. [1] Find, in terms of πand √ 3, (ii) the area of the shaded region, [3] (iii) the perimeter of the 9 The figure shows a circle, centre O, radius r cm. Give your answer correct to 3 significant figures. The lower arc is part of a circle with centre C and radius it. Nov 16, 2024 · The diagram: AB is an arc of a circle with centre O and radius 4 cm. [3] c) the perimeter of the segment bounded by the chord AB and the arc length of the sector. Indicate by marking points X and Y, the minor arc AXB and the major arc AYB of the circle. Find the are and perimeter of the shaded region, giving your answer in terms of π and 3 3) The diagram shows a sector OAB of a circle, centre O and radius x metres. 1a. in/question/963038. A curve has equation In the diagram, AB is an arc of a circle with centre O and radius 4 cm. . Triangle \( A O B \) is right angled and its hypotenuse \( A B \) is a tangent to the circle at \( P \) Angle \( B A O = x \) radians Find an expression for the length of \( A B \) in terms of \( \tan x \). Show that L= square root of 18-18cos θ . (9709/13/M/J/23 number 6) (a) Find the area of the shaded region. Calculate and justify your answer. The box is a prism of length 40 cm. Showing all necessary working, find the volume obtained when the region between the curve, the x-axis, the y-axis and the line x= 2, shown shaded in the diagram, is rotated through 360Å about the x-axis. The tangent at A and the tangent at 8 meet at the point C. The length of the fence is 63 m. [3] 9 In the diagram, AB and AC are tangents to a circle, centre 0 and radius 3. [2] (ii) Find the value of r. In the diagram, OAXB is a sector of a circle with centre O and radius 10cm. the expression for the length of PB. The arc DC, with centre 0, meets OA at C. The line OX passes through M. The diagram shows two arcs, A and B. 3cm. [3 marks] b) Find the area of the shaded region. PointsA and Blie on the circle and angle AOB=2θ radians. 8 be = युग C 6= $ 11 An arc AB subtends an Oct 15, 2017 · 6. The radius of the circle is 6 cm. [3] The diagram shows a semicircle, centre O, of radius 8cm. 498 radians, correct to 3 decimal places. B θ rad A O r cm 9π cm (i) Show that θ = 3π 5. Calculate, in terms of a°, the value of : ∠ACB, Give reasons for your answers clearly. The length of the chord AB is 12 cm. a Show that the arc length AB is 2x θ cos θ . Points C and D on OA and 0B respectively are such that the line AB is a tangent at E to the arc CED of a smaller circle also with centre O. the diagram shows a sector OAB of a circle with centre O and radius 5cm. The point P lies on OC and BP is perpendicular to OC. AB is a chord of the circle. a Find angle BAO in radians. 6, find the area of the shaded region. An arc equal in length to the radius of a circle subtends an angle of $1$ radian at the centre. i Find the total perimeter of the shaded regions. - с P2 Ograd 4 cm In the diagram, AB is an arc of a circle with centre 0 and radius 4 cm. [4] 4 The diagram shows a sector AOB of a circle with centre 0 and radius 5cm. The length of the arc AB is 8cm. ii For the case where r=5cm and θ =0. Solve math problems with the help of AI calculator and live tutors. The diagram below shows a circle centre O, with radius r. Oct 15, 2023 · MAY/JUNE 2017 9709/1 In the diagram, OAXB is a sector of a circle with centre O and radius 10 cm. Question: NOT TO SCALE 72° 9cm A The diagram shows a sector of a circle, centre 0, radius 9cm. 4 radians. Time: Duration: Period: Specific Objectives: At the end of the lesson, the students should be able to: i) Identify a circle and the centre of a circle. [4] The following diagram shows a circle with centre O and radius 3 . Aug 15, 2019 · 2. a Show that the radius of the arc CED is 3. Angle AOB is a radians. AB is an arc of a circle, centre O and radius r em, and angle AOB point X lies on OB and AX is perpendicular to OB. i Calculate the length of the arc DC. The diagram shows an arc ADC of a circle with centre O and radius 6 cm. Arc AB = 9π cm. Find the value of θ The diagram shows a sector OAB of a circle with centre O. The line OX passes through M, the mid-point of AB, and OX is perpendicular to AB. ii For the case where r=5 cm and θ=0. b Use your values of θ and r to find the area of T, giving () Find the values of mand. AB is an arc of a circle centre O. Unit topic: Circle theorem. 6 cm The diagram shows a sector OAPB of a circle, centre O. [3] (ii) Given that the area of region R 1 is 30cm2, find the area of region R 2, correct to 3 significant figures. Answer/Explanation The diagram shows a motif formed by the major arc AB of a circle with radius r and centre O, and the minor arc AOB of a circle, also with radius rbut with centre C. 131 12 and ?-r, find the perimeter of the shaded region AXB, leaving your 141 (ii) In the case where r answer in terms of V3 and ?. O. [2] 9 a Show that the equation 3tan 2x-3sin 2x-4=0 may be expressed in the form acos 4x+bcos 2x+c=0 , where a, b and c are constants to be found. The area of triangle AOB is 8cm2. The arc AB is part of a circle, centre O, radius r, and is of length 1. 9 i [4] Find an expression in terms of a for the perimeter of the shaded region ABDC. (a) Show that the angle AOB is 1. B 6 mark EP The diagram shows the sector 04B of a circle with centre 0. In the diagram, APB is an arc of a circle. A a rad В D 4 cm In the diagram, AB is an arc of a circle with centre O and radius 4 cm. The radius OC is perpendicular to the diameter AB. a Express angle ACB in radians. 6 The diagram shows a major arc AB of a circle with centre O and radius 6 cm. marks) 4. (a) Calculate the length of the arc AB. A and B are points on the circumference such that the arc AB forms an angle of 10 0 ∘ as shown. 2 radians. In the given figure, in a circle with centre O, length of chord AB is equal to the radius of the circle. i) Find an expression in terms of a for the perimeter of the shaded region ABDC. . The point X lies on A C and BX is perpendicular to A X. 3948 radians, correctto 4 decimal places. Question: 6 In the diagram,AC is an arc of a circle,centre O and radius 10 cm. In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords? Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C). The area of the shaded sector OAB is 21. The radius of the circle is 15 cm. Give your answer correct to one decimal place. (2) The points C and D are on the lines OB and OA respectively, with OC = OD = 30 m. Show that the area enclosed by the two arcs is equal to 25 (√ 3 − π 6) c m 2 The diagram shows points A, B and C lying on a circle with centre O and radius r. [41 (1) Find an expression in terms of a for the perimeter of the shaded region ABDC. The angle of the sector is 30 °. 5 radians. 5 The diagram shows a circle centre O and radius 5cm. a Find angle POQ, in radians. [3] In the diagram, A BC is a semicircle with diameter A C, centre O and radius 6 cm. OA = OB = 5. To learn more 1)If ABC is an arc of a circle and angleABC=135,then the ratio of arc PQR to the circumference is. [3] 0606/22/M/J/18 Q6i 34. Arc BC is part of a circle with centre A and radius 12cm, where AOC is a stralght line. The points A, B and C lie on the circle. ii. Area of arc = × 9. Find the value of θ. \) \( j _ { 1 } \) \( p \) Apr 14, 2024 · Solution For The diagram shows a sector OAB of a circle with centre O. The length of the arc A B is 15 cm. The length of the arc AB is 4r. Angle AOB=75° Length of arc AB=7. the area of the shaded region. Angle COD=1. A. 5r (a) Find, in radians, the angle AOB. (a) Find the value of θ. Give your answer correct to 3 Feb 24, 2018 · The diagram shows four straight lines AD, BC, AC, and BD. [3] In the diagram, AB is an are of a circle with centre O and radius . The angle-in-a-semicircle theorem can be generalised considerably. Calculate the size of angle AOB of The diagram shows a circle with centre O and a chord AB. b) find the area of the sector OAB In each diagram below, AB is an arc of a circle with centre O, and P is a point on the opposite arc. Question: 9. Chord AB has a length of 5 cm and AOB=θ Find the value of θ, giving your answer in radians. The length of the chord AB is 12cm. Show that L=18−18cosθ. The tangents to the circle atP and Q B The diagram shows a sector OBAC of a circle with centre O and radius 10cm. [5] In the diagram, AB is an arc of a circle with centre O and radius 4 cm. The points A, B, C and D lie on the circle such that the chord AB=15cm and the chord CD=10cm The chord AB is parallel to the chord DC. The length of the arc AB of the circle is 9πcm. 1. (a) State the size of angle ACO in radians. [3] ii Find the total area of the shaded regions. [3] (ii) In the case wherer = 12 and θ = 1 6 π, find the perimeter of the shaded region AXB Cambridge International AS & A Level Mathematics 9709 Paper 11 Q7 June 2 9 In the diagram, AB is an arc of a circle with centre O and radius 4 cm. 1 P The cone has volume 56. (5 marks) The diagram shows a circle with centre O and radius 34 cm. The minor arc AB is such that angle AOB is θ radians. 18. The length of the arc AB is 6 In the diagram, arc AB is part of a circle with centre O and radius 8 cm. Find an expression in terms of θ for the perimeter of the shaded region ABDC. B. Find AB 10. The arc also subtends the angle APB , called an angle at the circumference subtended by the arc AB . [3] the area of the segment bounded by the chord AB and the arc length of the sector. brainly. For the case where In the diagram OAB is a sector of a circle, centre O and radius Rcm, and ∠ AOB=2θ radians. iii. The arc AB is the major arc of a circle, centre O, radius 10. 2π a If 0 = 3 of i the area of the sector AOB ii the length of the arc AB. O is the centre of the circle which has a radius of 5. Area of arc = 27 × . The line AB is perpendicular to OA and OCB is a straight line. diagram not to scale Points A and B lie on the circumference of the circle, and Ahat OB=1 radian . (2. a Find the value of r. Aug 26, 2021 · The diagram shows a circle, centre O, radius 12 cm. The length of the minor arc AB is 6. Angle AOC= 1/6 π and the length of the arc AB is 2cm. Find the area of the segment enclosed by the chord AB and the minor arc AB, when: a 6=0. [4] (a) Find the perimeter of the shaded segment. The points A, B, and C lie on the circle. In the diagram, AB is an arc of a circle with centre O and radius 4 cm. [5] [4] (N13/22/10) O radius 8 cm. b Using ∠ OCE show that Rsin θ =r(1+sin θ ). The radius of the circle is 12 cm and angle AOB is 1. What is the total length of the rope that is used to mark the landing area? The diagram shows a semicircle with centre O and radius 6cm. The line AX is a tangent to the circle at A, and OBX is a straight line. iii Using the values 10 8 In this question all lengths are in centimetres. Arc B is part of the circle with centre M and radius PM, where M is the mid - point of PQ. It is given that angle ACB =80 ° . The arc DE with cent6re A and radius 2cm meets AC at D and AB at E . (2) The line AC shown in the diagram above is perpendicular to OA, and OBC is a straight line. The point D on OB is such that AD is perpendicular to OB. (i) Show that the exact length of AX is 6 √ 3cm. ED = 22 cm and DC = 18 cm. and are points on the circle so that the length of the arc is 5 cm. (1) AB=16cm (b) Work out the radius of the circle. i Express the perimeter of the shaded region in terms of r,θ and π. The line CD is parallel to AO and angle AOC=θ radians. The diagram shows a sector OAPB of a circle, centre O. DC is an arc of a circle with centre and radius The diagram shows a circle, centre O, radius 10cm. In the figure given A, B, C and D are four points on the circumference of a circle with centre O. (i) Show that θ = π−1. Arc BC is part of a circle with centre A and radius 12 cm, where AOC is a straight line. Calculation: According to the question. The arc BDC is part of a circle with centre A. The angle at the centre of the circle is 670. b Calculate i the length of AC, correct to 2 decimal places, ii the perimeter of the shaded region, iii the area of the shaded region. The perimeter of the shaded region is 12. A circle with centre C and radius R cm. [5] 7 1 3B rad O A C D 3cm 1 3 In the diagram, OADC is a sector of a circle with centre O and radius 3cm The diagram shows a sector of a circle with centre O. The mid-point of O A is P and ∠ A OB = 0. (7 mar diagram not to scale B A The points A and B lie on the circumference of the circle, and AÔB = 0. Arc BC is part of a circle with centre A and radjus 12 cm, where AOC is a straight line. Points C and D on OA and OB respectively are such that the line AB is a tangent at E to the arc CED of a smaller circle also with centre O. a Given that angle ACB=k π radians, state the value of the fraction k. (b) Find R in terms of r. A fence from a point A to a point B is in the shape of an arc AB of a circle with centre O and radius 45 m, as shown in the diagram. [3] (ⅲ) In the case where r=5 and θ =1. The diagram shows a shaded shape. i) Calculate the length of arc AB. Angle AOB is radians. The point Don OB is such that AD is perpendicular to OB. Useful Relations The diagram shows a major arc AB of a circle with centre O and radius 6 cm. b Find the value of \( x \) for which the two shaded areas are equal \( . ∠ AOB=2θ radius r cm touches the arc AB at T, and touches OA and OB at D and E respectively, as shown. the length of the arc A B. Arc length= cm [2] (b) Calculate the area of the sector AOB. The diagram shows a sector of a circle, centre O, radius 5r. The line AB is a tangent at E to the arc CED of a smaller circle also with centre O. The arcDC, The diagram shows a circle with centre . δ The diagram shows a circle, centre that A and B lie on the circle and the tangents at A and B meet at C. 2 cm. The line AB is of length 15, the line OC is of length 25 and the lengths of AC and BC are equal. The line BC is of length 2√3 cm and is perpendicular to AC. O, C, and D lie on a straight line. c. is a sector of a circle, centre O. The arc D C, with centre O, meets O A at C. The upper arc is part of the circle with centre 0 and radius r. (a) (b) Calculate the area enclosed by the rope. The length of AB is 4cm and angle CAB is \(\alpha\) radians. (1) Find the perimeter of the shaded region | 5| cm C In the diagram, D lies on the side AB of triangle ABC and CD is an arc of a circle with centre A and radius 2 cm. AB is an arc of the circle, centre O and radius 10cm, and CD is an arc of the circle, centre O and radius 20cm? The following diagram shows a circle with centre O and radius 8 cm diagram not to scale C The points A, B and C are on the circumference of the circle, and AOB radians. The point X lies on OB and AX is perpendicular to OB. 1b. Find: i. The arc BEC is part of a circle with centre P. 1 Calculate the length of arc AB AB using the formula for the arc length, which is \frac {\theta} {360^ {\circ}} \times 2\pi r 360∘θ ×2πr, where \theta θ is the central angle in degrees and r r is the radius. [4] A O B C E D A B C E D 12 cm 40 cm 22 cm 12 cm 18 cm NOT TO SCALE Diagram 1 Diagram 2 Diagram 1 shows a closed box. The following diagram shows a circle with a centre O and radius r сm. The point C lies on the arc AB and the point D lies on OB. The point D on O B is such that A D is perpendicular to O B. The lines PX and QX are tangents to the circle at P and Q, respectively. Calculate the value of r. Find the perimeter of the shaded region BXC. AB and CB are tangents to the arc and angle AOC=frac π 3. b Given that the area of the sector AOB is cm² and the length of the arc ABC is cm, find the exact T 3 value of T ii 0. It is given that the perimeter of the sector is 20 cm. Arc AB = 2 arc BC and ∠AOB = 108 0. Curved surface area of come =srl The cone is formed by joining OA and OB. Find the length of arc ACB. (a) A circle is divided into 6 sectors in such a way that the angles of the sectors are in arithmetic progression. (a) Given that angle ACB= kπ radians, state the value of the fraction k. Angle AOC-3 π radians. O/N 23/P11/Q6 The diagram shows a motif formed by the major arc AB of a circle with radius r and centre O, and the minor arc AOB of a circle, also with radius r but with centre C. The point O lies on the straight line CB such that CO=0. Jriangle OAB is equilatera Work out the length of arc In the diagram, AB is an arc of a circle with centre O and radius 4 cm. (a) Find an expression in terms of α for the perimeter of the shaded region ABDC. Question: A C arad 0 D 4 cm In the diagram, AB is an arc of a circle with centre O and radius 4 cm. Trigonometry: Arc Length & Sector Area PhysicsAndMathsTutor. Calculate angle BAC, which is obtuse. (i) Show that the area, Acm2, of the shaded region AXB is given by A = 1 2 r2(θ−sinθcosθ). (Total 6 marks) 80. The diagram shows a sector OAB of a circle, centre O. Find the area of the shaded region BDC, giving your answer in terms of π and Q3/11/M/J/13 square root of 3. 3. APB is an arc of a circle with centre C and radii AC and BC. Find measure of each of the following. Mar 9, 2023 · In the diagram, AB is an arc of a circle with centre O and radius 4cm. Arc A is part of the circle with centre O and radius OP. ii Find the perimeter of the shaded segment. Given that ∠APB = a°. [3] The shaded segment in the diagram is bounded by the chord AB and the arc AB. Give your answer correct to 3 significant figures. [3] iii Using your values of r and θ, find the area of the shaded region. The point C lies on the arcAB and the point D lies on OB. Show that θ =a+bsin θ where a and b are constants to be found. [4] 4037/11/M/J/21 18 4037/11/M The diagram shows a sector of a circle, centre C. radians. 4cm. i. A circle, centre C and radius rcm, touches the arc AB at T, and touches OA and OB at D and E respectively, as shown. The diagram shows a motif formed by the major arc AB of a circle with radius r and centre O, and the minor arc AOB of a circle, also with radius r but with centre C. If AOB is equilateral and AOB = 0 radians, write down the value of e. In the diagram. [2] (iii) Find the area of the shaded region. The angle AD = 600 and OA = 0B = 80m. Points P and O lie on the circle suc' cm C In the diagram, D lies on the side AB of triangle ABC and CD is an arc of a circle with centre A and radius 2 cm. area of the triangle BCO; length of the arc AB. (i) Show that angle AOB= 1/3 π radians. [AB] divides the area of the circle in the ratio 1:7. Arc APB is twice the length of chord [AB]. 2cm Calculate the area of the sector. Question: The diagram shows a sector OAB of a circle with centre O. Arc AB is part of a circle with centre O Angle COD= 1/2 π radians. 6 cm. Point Qlies on ABand OQ is an arc of a circle with centre B. Calculate the area of the sector. AB. The circle has centre O and radius 8 cm. Angle AOB is θ radians and is 3 times angle OBA. Hence, find the perimeter of the shaded segment ABC. Answer [3] 18 A B C 23° 13 cm 6 cm NOT TO SCALE In triangle ABC, AB = 6 cm, BC = 13 cm and angle ACB = 23°. 6cm and that the area of the sector OAB is 76. a Write down, in terms of R and r, the length of OC. The diagram shows a circle, centre O, with radius 4 cm. ∠BAO = 36° ∠BCO = 48° Concept used: The angle subtended on the centre of the circle is twice that of angle subtended by same arc on the circumference. b Find the length of PX. b Calculate the value of R_1. In the diagram, AB is an arc of a circle with centre O and radius 4cm. a Given that the perimeter of the sector is 6 times the length of the arc AB, find the exact values of θ and r. Show that the area enclosed by the two arcs is equal to 25 (√ 3 − π 6) c m 2 (8) 13 The diagram shows a circle with radius \( 1 \mathrm { cm } , \) centre \( O \). Angle AOB = 72° Calculate the area of the shaded segment APB. In the diagram, AB is an arc of a circle, centre O and radius rcm, and angle AOB = θ radians. (a) Find angle BAO in radians (b) Find the area of the shaded region (c) Find the perimeter of the shaded region. Lesson topic: Angle subtended at the centre of a circle is twice that on the remaining parts of the circumference. The area of the segment bounded by the chord AB and the arc AB is 7. Angle A = 29° Work out the size of angle B. Points A and B lie on the circumference of the circle and AÔB = θ, where 0 ≤ θ ≤ \(\pi \). Calculate the area of the shaded region, given that ZBOC = za radians. In the diagram, AOD and BC are two parallel straight lines. APB is an arc of a circle centre o and radius 12 cm; AQB is a semicircle with AB as diameter. The diagram shows a sector OAB of a circle with centre O and radius rcm. In each diagram below, AB is an arc of a circle with centre O, and P is a point on the opposite arc. The line CD is parallel to AO and angle AOC= θ radians. The angle of the largest sector is $4$ times the angle of the smallest sector. Given that the area is 74. The area of the sector AOB is 12cm2. B Write down expressions for the: area of the sector OAB: b. The are DC, with centre 0, meets OA at C. The arc AB subtends the angle AOB at the centre. O B A 4r 5r NOT TO SCALE The diagram shows a sector of a circle, centre O, radius 5r. Topic 9: Circular Measure 1. i Express the perimeter of the shaded region in terms of r, θ and π. com The diagram shows a circle with centre O and radius cm. ii For the case where a = 1 īt, find Dec 25, 2021 · One Radian. Angle AOB = θ radians. f… - brainly. $$ Draw a chord AB of the circle. The point C lies on the circle with centre O, a Given that angl ACB=kx radians, state the value of the fraction k. i Show that θ =frac 96r2. b. Show that θ = 3π/4. [3 marks] Jan 19, 2023 · 7. 7 radians. A and B are points on the circumference such that arc AB an angle of 1109. [1] (ii) Calculate the area of the shaded region. The tangents to the circle at A and B meet at 7 ( Express the perimeter of the shaded region in terms of r and θ. The diagram shows a sector, POQ, of a circle, centre O, with radius 4cm. 8 radians. 606cm^2 , find a) the size of angle AOB, in radians. Theme: Circle geometry. Working: Answers: (a) (b) (Total 6 marks) 15. Angle BOA= θ [1] a Show that θ =0. Aug 14, 2020 · This answer is FREE! See the answer to your question: the diagram shows a sector of a circle, center O,radius 5r the length of the arc AB 4r. Find in terms of \(\alpha \) (i)the area of the shaded region. 1 AB is an arc of a circle, centre O, radius 9 cm. (a) Find an expression in terms of a for the perimeter of the shaded region ABDC. The pointsP and Q lie on the circle, and the arc length PQ is 9cm. Question: In the diagram, AB is an arc of a circle with centre O and radius 4 cm. The area of the minor sector AOB is 48cm2. Angle ADC=0. 2 21. 6 cm B rcm 10 A chord AB subtends an angle of radians at the centre 0 of a circle of radius 6. The length of arc ABC is and . lines AC BD intersect at O such that angle AOB is #pi/6radians#. [4] In the diagram, arc AB is part of a circle with centre O and radius 8cm. i Given that the area of the major sector AOB is 7 times the area of the minor sector AOB, find the value of θ. e с A i. The diagram shows a sector AOB of a circle with centre O and radius 6cm. (1 mark) b Using OCE , show that Rsin θ =r(1+sin θ ). OA is 9cm and arc AB is 10cm (a) Find the size of the angle AOB. Angle AOB= θ radians and OP=AP=x. ⅱi Given also that the perimeter of the minor sector AOB is 20cm, show that the value of r, correct to 2 decimal places, is 7. [1] (b) Find the area of ABC ', giving your answer in the form kr^2 , where k is a In the diagram, O A B is a sector of a circle centre O and radius 8 cm. The following The diagram shows a circle with centre O and radius 10cm. jccavm outn ivbu atuzpq mhxaw ppivd gvjne nqp aram zntmxm