Foundation Level (Fail → Pass)

1. What is a chord of a circle? Draw a diagram to show one.

2. State the theorem about a line drawn from the centre of a circle to the midpoint of a chord.

3. State the theorem about a perpendicular line drawn from the centre of a circle to a chord.

4. In a circle with centre O, a perpendicular is drawn from O to the chord AB, meeting it at X. If AB = 12 cm, what is the length of AX?

5. Draw a diagram showing how a radius, a chord, and the distance from the centre to the chord form a right-angled triangle.

Intermediate Level (Pass → Credit)

6. Create a study guide for solving chord problems. It must explain the strategy of using the chord theorems to create a right-angled triangle and then applying Pythagoras' Theorem.

7. A chord of length 16 cm is 6 cm away from the centre of a circle. Calculate the radius of the circle.

8. The radius of a circle is 13 cm. A chord is drawn 5 cm away from the centre. Calculate the length of the chord.

9. In a circle of radius 10 cm, two parallel chords of length 12 cm and 16 cm are drawn on the same side of the centre. Find the distance between the chords.

10. Prove that equal chords in a circle are equidistant from the centre.

Advanced Level (Credit → Distinction) 

11. Two parallel chords of lengths 10 cm and 24 cm are drawn in a circle of radius 13 cm on opposite sides of the centre. Calculate the distance between them.

12. Give me a rider problem that uses the chord theorems and congruent triangles to prove a property about intersecting chords.

13. The length of the chord AB of a circle with centre O is 8 cm. The perpendicular from O to the chord meets the circle at Y. If XY = 3 cm, where X is the foot of the perpendicular on AB, find the radius of the circle.

14. AB and CD are two chords of a circle with centre O. The midpoints of AB and CD are P and Q respectively. If the chords AB and DC produced meet at M, show that ∠MPO and ∠MQO are supplementary.

15. A chord of length 24 cm is 5 cm away from the centre of a circle. Another chord is 12 cm away from the centre. Find the length of this second chord.