Foundation Level (Fail → Pass)

1. State the "Angle at the Centre" theorem. If the angle at the centre is 100°, what is the angle at the circumference?

2. State the "Angles in the Same Segment" theorem. Draw a diagram to illustrate it.

3. State the "Angle in a Semicircle" theorem.

4. If AB is the diameter of a circle and C is a point on the circumference, what is the value of ∠ACB?

5. In a circle with centre O, points A, B, and C are on the circumference. If ∠AOB = 80°, find ∠ACB.

Intermediate Level (Pass → Credit) 

6. Create a study guide with a problem-solving checklist for Angles in a Circle: 1. Look for a diameter, 2. Look for the centre, 3. Look for a bow-tie shape, 4. Use other geometry.

7. In a circle, a chord AB subtends an angle of 40° at a point X on the circumference. If Y is another point on the same arc, what is ∠AYB?

8. A, B, C, D are points on a circle. AC and BD are diameters. If ∠CAD = 30°, find the value of ∠ACB.

9. In a circle with centre O, if triangle AOB is an equilateral triangle, find the value of angle ACB.

10. Prove that opposite angles of a cyclic quadrilateral are supplementary (add up to 180°).

Advanced Level (Credit → Distinction) 

11. Give me a rider problem that combines the "Angle at the Centre" theorem with the properties of isosceles triangles (formed by two radii).

12. Two circles intersect at P and Q. A straight line APB is drawn to meet the circles at A and B. Another straight line CQD is drawn to meet the circles at C and D. Prove that AC is parallel to BD.

13. Give me a challenging rider problem that requires using all three circle theorems to find a final angle.

14. PQ is a diameter of a circle. The chord RS is produced to X. Prove that ∠PSX + ∠QRX = 180°.

15. In triangle ABC, the bisector of ∠A meets the circumcircle of the triangle at X. Prove that XB = XC.