Circle Theorems Standard Questions (G10)

Size: px

Start display at page:

Download "Circle Theorems Standard Questions (G10)"

Lorraine Day
6 years ago
Views:

1 Circle Theorems Standard Questions (G10) Page 1

2 Q1.(a) A, B and C are points on the circumference of a circle with centre O. Not drawn accurately Work out the size of angle x. (1) Page 2

3 (b) P, Q and R are points on the circumference of a circle with centre O. Not drawn accurately Work out the size of angle y. Give a reason for your answer. Reason (2) (Total 3 marks) Page 3

4 Q2.AB is a tangent to the circle. Write down the value of x. Give a reason for your answer. Reason... (Total 2 marks) Page 4

5 Q3. (a) AB is a chord of the circle. TA and TB are tangents to the circle. Work out the size of angle x. (2) Page 5

6 (b) The diagram shows a circle, centre O. C and D are points on the circumference. COE is a straight line. DE is a tangent. Work out the size of angle y. You must show your working, which may be on the diagram. (3) (Total 5 marks) Page 6

7 Q4.The diagram shows a circle, centre O. Not drawn accurately (a) Work out the size of angle x.... (1) (b) Work out the size of angle y (3) (Total 4 marks) Page 7

8 Q5. Points A, B, C and D are on the circumference of the circle. CDE is a straight line. (a) Work out the size of angle BCD. Give a reason for your answer. Reason... (2) (b) Work out the size of angle ABC. (1) (Total 3 marks) Page 8

9 Q6. PAQ and PB are tangents to the circle. AC = BC Work out the size of angle x. You must show your working which may be on the diagram (Total 4 marks) Page 9

10 Q7.(a) P, Q, R and S are points on the circumference of the circle. Work out the size of angle x. Answer... degrees (1) (b) The diagram shows a circle and a tangent at T. Write down the size of angle w. Give a reason for your answer. Answer... degrees Reason... (2) Page 10

11 (c) A, C and D are points on the circle, centre O. BA and BC are tangents to the circle. Work out the size of the angle y. Answer... degrees (3) (Total 6 marks) Page 11

12 Q8. (a) O is the centre of the circle. Write down the size of angle a. (1) (b) Write down the size of angle b. Give a reason for your answer. Reason (2) Page 12

13 (c) A, B, C and D are points on a circle, centre O. x + y + z = 290 Work out the values of x, y and z x =... degrees y =... degrees z =... degrees (3) (Total 6 marks) Page 13

14 Q9.(a) The diagram shows a circle, centre O. Work out the value of x.... (1) (b) The diagram shows a cyclic quadrilateral. Work out the value of y (2) (Total 3 marks) Page 14

15 Q10.A, B, C, D and E are points on a circle. AC is parallel to ED. (a) Write down the size of angle x. (1) (b) Work out the size of angle y (3) (Total 4 marks) Page 15

16 Q11. P, Q and R are points on a circle. Triangle PQR is isosceles. XY is a tangent to the circle at P. Work out the size of angle RPY Answer... degrees (Total 2 marks) Page 16

17 Q12. A, B, C and D are points on the circumference of a circle centre O. AC is a diameter. Angle DAC = 42 (a) Write down the value of x. Answer... degrees (1) (b) Work out the value of y. Answer... degrees (1) (Total 2 marks) Page 17

18 M1.(a) 35 (b) 100 Angle at centre twice angle on circumference Must use words centre and circumference (or perimeter ) Allow poor spelling even though both words given oe (strand) (i) Q1 [3] M2.43 Alternate segment (theorem) Strand (i) Do not accept Alternate Dependent on Q1 [2] M3. (a) (180 38) 2 M1 71 May be on diagram if no contradiction A1 (b) ODE = 90 seen or implied or CDO = 25 or COD = 130 Page 18

19 May be on diagram DOE = 50 or CDE = 115 or 140 seen May be on diagram 40 M1 A1 Additional Guidance 40 with no working seen 115 is M1 unless from clearly incorrect working e.g. 115 leading to an answer of 65 is M1 only M1A1 [5] M4.(a) 150 (b) or 210 or 360 their 150 oe OCA = 18 seen or implied or or 87 M or their 210 oe OCB = or 57 seen or implied or M1dep 57 A1 [4] Page 19

20 M5. (a) 108 Opposite angle of a cyclic quadrilateral Strand (i) (add up to 180) Must have 108 Additional Guidance Must see opposite and cyclic (oe e.g. quadrilateral in a circle) Q1 (b) 125 [3] M6. ABC = 52 May be on diagram M1 BAC = 52 or BAQ = 104 or ACB = 76 May be on diagram M1dep PAB = 76 or PBA = 76 May be on diagram M1dep 28 Clear evidence that 28 is for angle x A1 Page 20

21 Additional Guidance Angles may be on diagram ACB = 52 and ABC = 52 M1 only [4] M7.(a) 56 (b) 70 Alternate segment (theorem) Strand (i) Dependent on Q1dep (c) 2 47 or 94 or Angle BOA = 47 or Angle BOC = 47 or Angle BAC = 47 or Angle BCA = 47 May be on diagram (obtuse angle) M1 90 or right angle symbol seen at A or C or or ( ) 2 oe M1 Page 21

22 43 A1 [6] M8. (a) 35 (b) 40 Opposite angles of cyclic quad (add up to) 180 oe Strand (i) No need to mention 180 if angle given as 40 Accept supplementary to mean adds to 180. Q1 (c) x = 55 y = 110 z = 125 If answer line blank mark diagram or script. B2 any two correct B2 y = 110 and x + z = 180 B2 z = 125 and y = 2x any one correct values less than 180 such that y = 2x or x + z = 180 B3 [6] M9.(a) 70 (b) 4y + y = 180 or 5y = 180 oe or Page 22

23 M1 36 A1 [3] M10.(a) 70 (b) ADE = 34 or AED = or 110 or ADC = or 76 Angles seen on diagram must be in correct place M1 ADE = 34 and AED = or 110 M1dep 36 A1 [4] M (2 35) RQP = 110 marked on diagram 110 [2] Page 23

24 M12. (a) 42 (b) 48 [2] Page 24

Properties of the Circle

9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference