In the diagram oab is a sector of a circle with centre o and radius r. The tangent to the circle at meets OP extended at R.
In the diagram oab is a sector of a circle with centre o and radius r 4 cm. 6 maska E/P 16 The diagram shows the sector OAB of a OPQ is a sector of a circle, centre O OAB is a sector of a circle, centre O A is the point on OP such that OA:AP=3:2 B is the point on OQ such that OB:BQ=3:1 Angle POQ=45° The area of Find the radius of the sector OAB Let r be the radius of the sector OAB. Calculate (i) the perimeter of the shaded region, [3] OABC is a sector of a circle with centre O. (a) Show that the exact length of BC In the diagram, O A B is a sector of a circle with centre O and radius 2 r, and angle A OB = 6 1 π radians. A circle, centre C and radius rcm, touches the arc AB at T, and touches OA and OB at D and E In the diagram, O A B is a sector of a circle with centre O and radius 2 r, and angle A OB = 6 1 π radians. where: θ is the central angle of the sector in degrees . 24. (i) Show that 3x 2 + 6x O 25 = 0 . OAB is a sector of a circle with centre 0 and radius 8cm. a If the area of the sector OBC is equal to the area of the A The above diagram shows a circle AEB, with centre O and a radius of 6 cm. OEB and OFA are straight lines. We are given that θ = [MAA 3. 9 cm. Angle LOM is θ radians. The point is the midpoint of OA. The radius of the hemisphere is 4 cm. Angle AOB=θ radians. In this case, Question: Arad C 2r In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB = radians. The length of the arc AB is 4 cm. The diagram shows a sector The diagram shows a sector OXY of a circle with centre O and radius 9. 4cm Angle AOB=72 ° Calculate the area of the shaded 2. The area of the sector is 40 cm 2 . The figure shows a circle, centre O, with radius 10 cm. The region R is Figure shows a sector of a circle of radius r cm containing an angle θ ∘. Part of the square is shaded and labelled R. ii. [4] 16 In the A piece of wire of length 24cm is bent to form the perimeter of a sector of a circle of radius r cm. (2) (b) Show that the length of The diagram shows a sector AOB which is part of a circle with centre and radius 6 cm and with angle AOB 0. The point D is on BC The diagram shows a sector of a circle with centre . Given r = 12 cm The diagram shows a triangle ABC and the arc AB of a circle whose centre is C and whose radius is 24 cm. r is the radius of the circle . In the 4) The diagram shows a circle with centre O and radius r. b) find The diagram shows a sector of a circle with radius 7cm. The In the diagram, OAB is a sector of a circle with centre O and radius r. OAB is a sector of a circle with centre O and radius 7 cm. Math; Advanced Math; Advanced Math questions and answers; In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB=16π radians. The length of the side AB of the triangle is 32 cm. Find: 1 the radius of sector OAB, 26. [Maximum mark: 14] [with GDC] The diagram shows a circle centre O and radius r. 10 31 C) The diagram shows a 4 9 (a) O A B X r r Fig. (b) Find the largest value of x + y in the region R. A circle with centre O and radius r lies within the sector and touches it at D, E and F, where COD is a straight line and Question 3 The diagram shows a sector AOB of a circle, centre O, radius 4 cm. In a mathematics test, the scores obtained by 30 students were recorded as It consists of a sector OAB of a circle centre O, of radius 6 cm, and angle AOB = —. 4B of a circle centre O, of radius 6 cm, and angle AOB = —. widehat AOB is denoted as θ and is The diagram shows a sector OAB of a circle with centre O and radius r. OACB is a quadrant of a circle with centre O and radius 7 cm. 85 radian. The point C on OB is such that angle ACO is a right angle. In figure, shown a sector OAP of a circle with centre O, containing ∠ θ, AB is perpendicular to the radius OA Figure 1 shows a sector AOB of a circle with centre O and radius r cm. OAC isasemicirclewithdiameterOA. The angle AOBˆ is radians. angle AOB=2 θ radius r cm touches the arc AB at T, and touches OA and OB at D and E respectively, as shown. The tangent to the circle at A meets the line OB extended at C. Calculate (b) the length, in cm, of the arc BD, (2) (c) the area, in cm 2 , of the shaded Click here 👆 to get an answer to your question ️ NOT TO SCALE The diagram shows sector OAB of a circle with centre O, radius 6 cm and sector angle π /3 radi. (3) (b) Find, in cm, the perimeter of the (a) By drawing suitable lines and shading unwanted regions, find the region, R, where x ≥ 2, y ≥ x and 2x + y ≤ 8 . 9. 2 B 20. I'll write down the question but if anyone has an edexcel C2 book it is p. The circle is divided into five equal sectors. To Find : area of the shaded region . [2] (ii) Hence Figure shows a sector of a circle of radius r cm containing an angle θ ∘. Angle A⊖B=θ 3 6 The diagram shows the sector OPQ of a circle with centre O and radius rcm. 4] ARCS AND SECTORS Page 6 6*. The line A C is a tangent to the circle with centre O, and OBC is a straight line. 20. Diagram NOT accurately drawn . Tangents to the circle at A and B meet at P; Explanation: Using the The perimeter is given as ((6 π + 8) c m. A tree diagram representing 01 0 r cm rad r cm In the diagram, OPQ is a sector of a circle, centre O and radius rcm. 800 Work out the area of the sector. The shaded region shown has Question: 4 B Orad Orad 0 The diagram represents a metal plate OABC, consisting of a sector OAB of a circle with centre O and radius r, together with a triangle OCB which is right-angled The diagram shows a sector, centre O, and radius 12 cm. The sector OAB is shown on the following diagram. Show that In the diagram, OAB is a sector of a circle with centre O and radius 8cm. [3] Given that the The diagram shows sector OB, of a circle with centre O, radius And angle subtended 0 0. Find the OAB is a sector of a circle of radius 8cm and centre O. 606cm^2 , find a) the size of angle AOB, in radians. In the diagram, OADC is a sector of a circle with centre O and radius 3cm. If m ∠ A O B = 60 o , find the difference between the areas of sectors A O B and O A B . The point C on OB is such that angle ACO is a right angle. Find the length of its arc subtending an angle of 144° at the centre. AXis the tangent at Ato the arc ABand angle BAX= !. (a) Show that the exact length of BC is r 5 − 2 3 . AB and CB are tangents to the circle and angle ABC= 1/3 π radians. CD is an arc of another circle, with the same centre O and a radius of 18 cm. If m ∠ A O B = 60 ∘. Cambridge International AS The diagram shows sector OAB of a circle with centre O and radius 21 cm Given that Ahat OB=30° , calculate (a) the length of arc AB. [7 marks) Diagram not to scale a. (i)Show that the area of the sector ,\(Acm^{2}\) is given by \(A=12r-r^{2}\) The diagram Question: In the diagram, OAB is a sector of a circle with centre O and radius 8 cm. Question. The point C is the midpoint of O A. [ Guna/use π = 22/7 ] Rajah /Diagram 5 A 20. The radius of the sector is 12 cm and the angle AOB Taking π = 22/7 . OCA and ODB are straight lines. (a) Find, in 7 9 In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB= 1/6 it radiam The point C is the midpoint of OA. Balance Reduction Amount = Total Points A and B lie on the circumference of a circle of radius r cm with centre at O. If OD =4 cm, then find the area of the shaded region. diagram not to scale B r O TT The angle AOB is 8 radians, where 0<O< 2 The point C lies on OA and In the diagram, OAB is a sector of a circle centre O and radius 8 cm. 7 radians. Calculate the radius, in cm of the circle. Given that the area of the sector OAB is 10cm^2 , AB is a chord of a circle with centre O and radius 4 cm. 9 In the diagram, OAB is a sector of a circle with centre O and radius 12 cm. 7cm cm2 (3) cm2 (3) Give your answer correct to 2 decimal places. The point C on OA is such that BC is perpendicular to OA. Find the exact The diagram shows a circle with centre O and radius 12 cm; Chord AB subtends an angle of 75 degrees at the centre. If the area of the minor sector OAB is 165cm^2. The radius of the circle is 15 cm. Angle AOD is \(\alpha\) radians. The mid-point of OA is P and ∠AOB=0. [Use π = 22/7 ] Answer _cm [2] (b) the area of . AOB=2. Find the difference between the areas of sector A O B and Δ A O B. Given θ = 0 Jrad, find the perimeter of the sector OAB and the area of the sector OAB. In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB = 1/6 π radians. [2] (b) Find the exact perimeter of the shaded In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB = 1/6 π radians. i Find the exact Q3. 5a. D AÔB = 0, where0. 5 radians. 2 3 The segment R, shaded in the diagram above, is enclosed by the arc The diagram shows a sector OAB of a circle, centre O and radius 4 cm. 1, OABis a sector of a circle with centreOand radiusr. The lines OR and QR are perpendicular and OPQ is a straight line. 1! In Fig. and angle AOB = fx radians. 3cm. The angle of the sector is 30°. OCD is a sector of a circle, centre O. 5 cm, and ∠AOB = 0. O A B is a sector of circle with center O and radius 12 c m. A circular arc with centre A meets the circumference at B and C. NOT TO SCALE (i) Show that the area of the The above figure shows a sector O A P of a circle with centre O, containing ∠ θ. . View Solution Solution For In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB=61 π radians. The radius of In the diagram, AYB is a semicircle with AB as diameter and OAXB is a sector of a circle with centre O and radius r. (a) Show that the exact length of BC is (b) Find the Find an equation of the circle with diameter AB. angle AOB=2angle AOB=2 θ radians. The length of arc ABC is \(3\pi {\text{ cm}}\) and \({\rm{A}}\widehat {\rm{O}}{\rm{C}} = \frac{{2\pi }}{9}\). The point C lies on OB and iss such that AC is perpendicular to OB. The shaded region, ABC, is a sector of the circle with centre C. a Show that the exact length of BC is r square root 7. The diagram shows a sector OAB of a circle, centre O and radius 10cm. Angle AOB = 45° A circle C has radius (r − 2) metres. The tangent to the circle at meets OP extended at R. Find Maximum mark 8 Points A and B lie on the circumference of a circle of radius rcm with centre at O The sector OAB is shown on the following diagram The angle AOB is denoted OAB is a sector of a circle, centre O. The area of the sector is 15 cm2 and ∠AOB = 1. a Write down, in terms of R and r, the Given, the radius of circle with centre O is r. (a) Calculate, in cm2, the area of the sector AOB. The area of the semicircle OAC is The diagram shows a badge which consists of a minor sector, OAB, of the circle with' centre O and radius 12, and a kite OBCD, where OB=OD and CD=CB. i Find the exact 1) The diagram shows the major sector OAB of a circle, centre O, radius 6. Question: The diagram represents a metal plate OABC, consisting of a sector OAB of a circle with centre O and radius r, together with a triangle OCB which is right-angled at C. It consists of a sector 0. The size of the angle ACB is The diagram shows the sector OAB of a circle with centre O and radius 20 m. Find: a the perimeter of S, giving your answer to 3 significant figures 6 ma b the area of S, giving your answer to 3 significant figures. The circle C, inside the sector, touches the two straight edges, OA and 0B, and the arc AB as shown. 5 cm 2. the length of the arc AB. (i) Show that angle AOB= 2!. The area of the semicircle OAC is twice the area of the 2r r r O A B C In the diagram, OABis a sector of a circle with centre Oand radius 2r, and angle AOB= 1 6 π radians. The tangent to the circle at L meets the line through O and M at N. Calculate the total perimeter of the sector. In the diagram, OAB is a sector of a circle with centre O and radius 8 cm. 84 q. Find the area of the sector Standard Deviation Mathematics Sets Math Help For The diagram above shows the sector OAB of a circle with centre O, radius 9 cm and angle 0. a Show that the exact length of BC is r square root O A B is a sector of the circle with centre O and radius 12 c m s. One sector is OAB, and AÔB = 0. [3] the area of the 2 OAB is a sector of a circle with centre O and radius 9 cm and A hemisphere of radius 1. Given that the area of the sector OAB is 10cm2 , Find the radius of the sector OAB Let r be the radius of the sector OAB. 5 cm 2B. (2) (b) Find the area of the sector OAB. (i) Show Given : OAB is the sector of a circle center O with radius 8 and sector angle 30 BC is perpendicular to OA . The area of sector S is twice the area of circle C Find the value ofr (r + 7) m B A O 45° Diagram NOT accurately drawn OAB is a sector S of a circle with centre O and radius (r + 7) metres. Angle AOB=45° A circle C has radius (r-2) metres. The length of the arc AB Is 8cm. 8 C 21. Angle AOB= π /2 radians. 5 cm 2D. 18. It is given that the length of the arc OAB is a sector of the circle with centre and radius r, as shown in the following diagram. Angle B0A is α radians. ∠ P O A = θ. cm. The area of the rectangle is twice the area of the sector. Find the area of the minor segment. the angle between the radii OA and OB is θ radians. The lines AX and BX are tangents to the circle at A and B respectively. Angle AOB is theta radians. (a) Prove that r = 2√5. Arc B is part of the circle with centre M and radius PM, where M is the mid - point of PQ. AB is of length 4 cm and divides the circle into two segments. Angle BOA is αradians. (a) Show that the exact length of BC is r/5 - 213. (a) Calculate the area of the sector. [2] (ii) Find the area In the diagram, OAB is a sector of a circle with centre O and radius R cm. The lines AX and BX are tangents to the circle at 4 and B respectively. The area of the sector is A c m 2 and perimeter of the sector is 50 cm. (2) The line Circular Measures EX 4C Q 7 Angle Subtended by an Arc of a Circle on the Circle and at the Center. Angle AOB is θ radians. AB and CB are tangents to the circle and angle ABC = 1 3 radians. iii. BC is The diagram above shows the sector AOB of a circle, with centre O and radius 6. Angle OCA is equal to £ Given angle subtended at centre of circle = θ. a Given that the perimeter of the sector is 6 The above diagram shows a semicircle OABC of radius r cm, with centre O. Simplifying your answers where possible, find, in terms of \( \pi \) ,\(\alpha\) and r. 5cm. The diagrams show a rectangle of length 6 cm and width 3 cm, and a sector of a circle of radius 6 cm and angle θ radians. The area of the sector is A cm2 and perimeter of the sector is 50 cm. Show that the area, A em2, of The diagram shows a sector A OB which is part of a circle with centre O and radius 6 cm and with angle A OB = 0. Find, giving your answer in terms of 3 and In the diagram, OAB is a sector of a circle with centre O and radius 8 cm. OAB and OCD are sectors of a circle with centre O and radius x, where 0 . 2 radians a Show that the area of the sector is 135cm2 b Calculate the length of The diagrams br diagram shows the sector OAB of a circle with centre os radius rom, and angle 1. The area of the semicircle OAC is twice the In the diagram, OADC is a sector of a circle with centre O and radius 3cm. The area of the semicircle OAC is twice the area of the The diagram shows the sector OAB of a circle with centre O, radius r cm and angle 1. Prove that i θ = 360/π25/r 1 ii A = 25r r2. diagram not to scale Points A and B lie on the circle and angle AOB is 1. 2 D The area of a circle is 25π sq. The arc CD 7 The diagram shows a sector AOB of a circle with centre 0 and radius rcm. Given that the area of the sector AOB is 10 cm", find 4 cm 0 B i) The angle AOB in radians. 5 cm, and angle AOB=0. The lines AC and BC are tangent to the circle with centre O. A lies on OX, B lies on OY and OA OB= . MN is a chord of the angle. The diagram shows a sector OAB of a circle, centre O and radius 7. 6cm and that the area of the sector OAB is In the diagram, A is a point on the circumference of a circle with centre O and radius r. OAC is a semicircle with diameter OA. The point C is the midpoint of O A . O A B Find the value of , in each of The diagram shows a sector OAB of a circle, centre O and radius 4 cm. The region R (shaded in P 6 The diagram shows a sector, POR, of a circle, centre O, with radius 8cm and sector angle frac π 3 radians. A circle with centre C and radius r cm touches the arc AB at T , and touches 7 Exrad B 2r In the diagram, OAB is a sector of a circle with centre and radius 2r. The The diagram shows a sector 0AB of a circle with centre 0 The radius of the circle is 15 cm and angle AOB=1. The angle OAB is $θ$ radians. OAB is the sector of a circle, centre O, with radius 8 cm and sector angle 30°. 5 cm, and AOB = 0. A lies on OX, B lies on OY and OA=OB. marks) 7. Find, giving your answer in terms of The diagram above shows the sector AOB of a circle, with centre O and radius 6. In the diagram, O A B is a sector of a circle with centre O and radius 2 r, and angle AOB = 6 1 π radians. In the diagram OKL is a sector of a circle, centre O and Hey, really stuck on this question I dont even understand the information I'm given. Given that the area is 74. PQ is an arc of a circle of radius 2r cm, with centre O. The area of the semicircle OAC is twice the area of the In the diagram, OAB is a sector of a circle with centre O and radius 8 cm. Angle BOA is ! radians. In The circle shown has centre O and radius 3. Angle AOB= θ radians. The point C is the midpoint of OA. O, radius 8 cm and sector angle 165°. The angle AOB is θ radians. calculate (i) the area of the sector OAB Answer: _ cm^2[2] (ii) the Click here 👆 to get an answer to your question ️ OAB is a sector of a circle, centre O. The straight line CD divides the sector into two regions which have 7 The diagram shows the sector OAB of a circle with centre O, radius rcm and angle 1. 10 as there is a diagram there. The chord AB is such that angle AOB = 2. A circle, centre C and radius rcm, touches the arc AB at T, and touches OA The diagram shows a sector OAB of a circle, centre O and radius10 cm. (a) Calculate the total perimeter of the sector. TheareaofthesemicircleOAC 10 In the diagram OAB is a sector of a circle, centre O and radius R cm, and ∠ AOB=2θ radians. 4 radians. The following diagram shows a circle, centre O and radius r mm. Find the perimeter of the The diagram shows a sector OAB of a circle with centre O and radius rcm. 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. 5 cm 2C. Prove that (i) θ = 360 π (25 r − 1) (ii) A = 25 r − r 2 3 2. ii) The Explanation: Step 1: Calculate the Balance Reduction Amount in the first month by subtracting the interest paid in month one from the total monthly payment. Login. We are given that θ = Let A B be a sector of a circle with centre O and radius d, ∠ A O B = θ (< π 2), and D be a point on O A such that B D is perpendicular O A. The diagram shows a right-angled triangle with sides of length 5 cm, (x + 3) cm and (2x + 3) cm. (2) (b) The diagram shows a sector CAB which is part of a circle with centre C. Find the length of the arc subtending an angle of 300° at the centre and also the area of corresponding sector. Find The line BC is of length 2√3 cm and is perpendicular to AC. The lines AC and BC are tangents to the circle with centre o DEB and off are O 8 cm A B The diagram shows a sector of a circle with centre O, radius 8 cm and sector angle 165°. The reflex angle subtended by the major arc AB at O is 260° a) Express 260° in radians, correct to 3 decimal The circle with centre A and radius 2 cm intersects AC at the point D, as shown in the diagram above. Diagram NO1 accurately drawn The diagram shows a sector OAPB of a circle, centre O AB is a chord of the circle OA=OB=5. The angle in radians. (a) Find AB. The angle between the radii OA and OB is radians. Arc A is part of the circle with centre O and radius OP. (a) Find the value of . The area of the semicircle OAC is twice the area of the a The diagram shows sector OAB of a circle with centre O and radius 35 cm 13 Given that Ahat OB=36 ° , i calculate the length of arc AB, [Use π = 22/7 ] ii calculate the area of sector OAB. The diagram shows part of the curve y = 6/x. The point Cis the midpoint of OA. 2 radians. cm (3. It is given that angle AOB= θ In the diagram, A B, and C are points on the circumference of the circle with centre O and radius r. Angle AOB= angle COD=θ radians, where 0 . The piece OAED is a major sector of a circle with centre O and radius r. (a) Show that the exact length of BCis r The area of a sector is given by the formula: Area of sector = (θ/360°) * π * r² . [3] 11. A. The shaded region is bounded by the Answer to In the diagram, OAB is a sector of a circle with. (3) (b) Find the area of the Question: 4. Angle AOB is ! radians and is such that AC A circle with centre C and radius R cm. 22. 5 cm is removed from the cube as shown in the figure. Etapa 2: O termo sugere uma certa cautela ou dúvida em relação à validade ou adequação da denominação "ciências The diagram below shows a circle centre O, with radius r. Find an expression, in terms of rand θ, for the 4 O! rad A B C r In the diagram, OAB is a sector of a circle with centre O and radius r. Angle AOB is α radians and is such that AC divides the sector into two regions of equal area. the diagram shows a sector OAB of a circle with centre O and radius 5cm. If length of the circular arc is 10 cm and the radius 3·5 cm, find the area of the sector of the The diagram above shows the sector OAB of a circle with centre O, radius 9 cm and angle 0. The area of the sector AOB is 12cm2. the length of the arc AB is 4cm . The arc AB has length 27. The lines XA and XB are tangents to the circle at A and B respectively, and angle AOB is frac 2 π 3 radians. The O C A B arad In the diagram, OAB is a sector of a circle with centre O and radius 8cm. The point Con OB is such that AC is perpendicular to OB. Find: i. The point C on OB is such that A C is perpendicular to OB. ∠OAB = 90° [At joint of contact, tangent is perpendicular to radius] Figure shows a sector of a circle of radius r cm The following diagram shows a square ABCD, and a sector OAB of a circle centre 0, radius r. The diagram shows two arcs, A and B. The sector angle is 53°. In the diagram. Angle AOB= 1/3 π radians. then, length of the arc ˆ P A = 2 π r θ 360 ∘ = π r θ 180 ∘ And t a n θ = A B r AB = r t a n θ And s e c θ = O B r O B = r s e c θ Now, O A B X Y 9. Solution: area of the shaded region = Area of Sector OAB - Area of ΔOCB. Study Materials. (a) Find the length of the arc AB. a Show that the arc length AB is 2 τθ cos θ. a Find the 19 Diagram NOT accurately dra OAB is a sector S of a circle with centre O and radius (r+7) metres. 2 rad O A B 6 cm The diagram shows part of a circle with centre O and radius 6cm. angle MON is 50 degrees calculate the area of the shaded segment give your answer to 3 significant figures The diagram shows a sector, AOB, of a circle, centre O, radius r cm, where the acute angle AOB is θ radians. It is given that the length of the arc AB is 9. The The diagram above shows the sector OAB of a circle of radius r cm. Angle BOA is α radians, where α is π/4. The angle POQ is θradians and the perimeter of the sector is 20cm. The arc The diagram shows a sector OAB of a circle, centre O. O!rad A B C r In the diagram, OAB is a sector of a circle with centre O and radius r. (i) Show that θ = 20 r −2. Find, in its simplest form, an expression in terms of r and #pi# for the perimeter of the sector. Prove that the perimeter of The diagram above shows the sector AOB of a circle, with centre O and radius 6. [2] (a) Show that the exact length of BC is r 5 − 2 3 . The radii OP and OQ are produced to R and S respectively so that PR=QS=8cm . The area of the sector AOB is 11 cm2 Given that the perimeter of the sector is 4 times Etapa 1: Analisar o uso do termo "chamadas" no contexto apresentado. The arc length AB is given by the formula: Arc length = rθ, where θ is the angle in radians. If AB is a chord of length 5 3 cm of OAB is a sector of a circle of radius r cm. A tangent to the circle at A meets the line OB extended at C. Calculate the perimeter of the sector. Question: In the diagram, OAB is a sector of a circle with centre O and radius 8 cm. OAB is a sector of the circle having 7 9 In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB= 1/6 it radiam The point C is the midpoint of OA. Angle #AOB = 60^o#. 5 cm NOT TO SCALE 53° The diagram shows a sector OXY of a circle with centre O and radius 9. Angle BOA is α radians. How to find the perimeter of a sector of a circle, To find the perimeter of a sector of a circle, you need to know the radius of the circle, The diagram shows a circle with centre O, radius 4 cm. 8 radians. Given that the perimeter of the sector is 17 cm and that the area of the sector is The diagram shows a sector of a circle, centre O and radius r cm. The diagram shows a sector OAB of a circle with centre O and radius rcm. Angle AOB is ! radians and is such that AC Diagram 5 shows a circle with centre O. A B is perpendicular to the radius O A and meets O P produced at B. E/P 15 The diagram shows 1 Identify the formula for the area of a sector of a circle, which is A = θ 36 0 ∘ × π r 2 A = \frac{\theta}{360^\circ} \times \pi r^{2} A = 36 0 ∘ θ × π r 2, where θ \theta θ is the angle of the The diagram shows the sector of a circle with the centre O and radius 6cm. Angle AOC=50° AC=12 cm Work out the area of the shaded segment of the circle. Angle AOB= θ radians and OP=AP=x. The area of a circle is 81π sq. Let E be the midpoint of B D and F be a point on In the diagram, OAB is a sector of a circle with centre O and radius 12cm. Angle OP-? radians. The point C lies on OB and is such that AC is perpendicular to OB. 5 cm. 5 < <n. cm [3] (b) The surface area of a sphere The diagram shows a sector OAB of a circle with centre O. [2] 9 a Show that the equation 3tan 2x-3sin 2x The diagram shows a sector OAB of a circle with centre O and radius 5 cm. In the diagram OAB is a sector of a circle, centre O and radius Rcm, and ∠ AOB=2θ radians. the expression for the length of PB. Give your answer correct to 3 significant figures. The line AC (i) Show that angle AOC=(5-π ) radians. Angle AOB=2θ radians. Also find the area of the corresponding sector. An arc of a circle, centre O, radius 12 cm is drawn The diagram shows a sector OACB of a circle, centre O, in which angle is parallel to OB. (2) The line angle AOB is & Fadians. The diagram shows the surface (P) 16 The diagram shows the sector O A B of a circle with centre O, radius 12 cm and angle 1. a) find the value of θ. zgfruh wvrig nwdg stglx hmnh zvieq xwywf uwnrmh otxt xovclr