| 1 | (2018/w/21/q13) The diagram shows a triangle ABC and an arc with centre C and radius 6.5cm. (a) Using a straight edge and compasses only, construct the locus of points inside the triangle that are equidistant from BA and BC. (b) Shade the region inside the triangle that is • more than 6.5cm from C and • nearer to BA than to BC. |
(a)2 (b)1 |
|---|---|---|
| 2 | (2017/m/22/q2) The line AB is one side of an equilateral triangle ABC. Using a straight edge and compasses only, construct triangle ABC. |
2 |
| 3 | (2017/s/22/q16) (a) Using a straight edge and compasses only, construct the bisector of angle BAC. (b) Shade the region inside the triangle that is nearer to AC than to AB |
(a)2 (b)1 |
| 4 | (2017/w/22/q3) In the diagram, BL is the bisector of angle ABC and MN is the perpendicular bisector of AB. Complete the statement. The shaded region contains the points, inside triangle ABC, that are • nearer to B than to A and • nearer to ....................... than to ....................... | 2 |
| 5 | (2018/s/22/q9) Using a straight edge and compasses only, construct the locus of points that are equidistant from A and B |
2 |
| 6 | (2017/s/21/q21) A, B, C and D are points on the circle. AD is parallel to BC. The chords AC and BD intersect at X. Find the value of u and the value of v. (b)  F, G and H are points on the circle, centre O. Find the value of p. |
(a)3 (b)2 |
| 7 | (2017/s/22/q26) A, B, C, D and E lie on the circle. AB is extended to F. Angle AED = 140° and angle CBF = 95°. Find the values of w, x and y |
5 |
| 8 | (2017/w/22/q22) A, B, C and D are points on the circle, centre O. BCE is a straight line. Angle AOC = 108° and angle DCE = 60°. Calculate the values of w, x and y. |
2 |
| 9 | (2018/m/22/q14) A, B, C and D are points on the circumference of the circle. AC and BD intersect at X. (a) Complete the statement. Triangle ADX is ..................................................... to triangle BCX. (b) The area of triangle ADX is 36cm2 and the area of triangle BCX is 65.61cm2. AX = 8.6 cm and DX = 7.2cm. Find BX. |
(a)1 (b)3 |
| 10 | (2018/s/22/q16) The diagram shows a circle, centre O. AB is a chord of length 12cm. M is the mid-point of AB and OM = 4.5 cm. Calculate the radius of the circle. |
3 |
| 11 | (2018/w/22/q2) The diagram shows a circle, centre O. AB and DE are chords of the circle. M is the mid-point of AB and N is the mid-point of DE. AB = DE = 9 cm and OM = 5 cm. Find ON. |
1 |
| 12 | (2017/w/23/q22) In the diagram, points A, B, C, D, E and F lie on the circumference of the circle. Angle BFC = 19°, angle ADB = 23° and angle ABE = 67°. Work out (a) angle BEC, (b) angle ABC, (c) angle BCE |
(a)1 (b)3 (c)2 |
| 13 | (2018/s/23/q20) The points A, B, C, D and E lie on the circumference of the circle. Angle DCE = 47° and angle CEA = 85°. Find the values of w, x and y. |
3 |
| 14 | (2018/s/42/q9) (a)  A, B, C, D and E lie on the circle, centre O. Angle AEB = 35°, angle ODE = 28° and angle ACD = 109°. (i) Work out the following angles, giving reasons for your answers. (a) Angle EBD = ............................. because ........................................................................... (b) Angle EAD = ............................. because ........................................................................... (ii) Work out angle BEO. (b) In a regular polygon, the interior angle is 11 times the exterior angle. (i) Work out the number of sides of this polygon. (ii) Find the sum of the interior angles of this polygon. |
(i)(a)3 (b)2 (ii)3 (b)(i)3 (ii)2 |
| 15 | (2018/w/42/q7) In the diagram, A, B, C and D lie on the circle, centre O. EA is a tangent to the circle at A. Angle EAB = 61° and angle BAC = 55°. (a) Find angle BAO. Angle BAO = ................................ (b) Find angle AOC. Angle AOC =................................. (c) Find angle ABC. Angle ABC = ................................. (d) Find angle CDA. Angle CDA = ................................ |
(a)1 (b)2 (c)1 (d)1 |
| To be continued... |
1. (a) Correct angle bisector at B with two pairs of correct arcs reaching AC (b) Correct region shaded
2. Equilateral triangle with correct arcs
3. (a) Correct bisector with correct arcs (b) Correct region shaded
4. BC AB
5. Correct perpendicular bisector of AB with 2 pairs of correct arcs
6. (a) \( u=35, v=110 \), (b) 75
7. \( w=40, x=95, y=45 \)
8. \( w=54, x=126, y=60 \)
9. (a) similar (b) 11.61
10. 7.5
11. 5
12. (a) 19 (b) 138 (c) 90
13. \( w=95, x=85, y=48 \)
14. (a)(i)(a) 62 and Isosceles [triangle] and Angle at centre is twice angle at circumference (b) 62 and [Angles in] same segment or angle at centre is twice angle at circumference (ii) 8 (b)(i) 24 (ii) 3960
15. (a) 29 (b) 128 (c) 64 (d) 116
16. (a)(i)4 (a)(ii)36.9 or 36.86 to 36.87 (b) \( [v= ] 150,[w=] 15,[x=] 15,[y=] 10(\mathrm{c}) 182 \) or 182.4. . .
17. 165
18. 101
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