Circle theorem

Task goals

• State and apply the tangent-radius theorem (90 degrees at the point of contact).
• State and apply the angle-in-a-semicircle theorem (90 degrees).
• Use the same-segment theorem to identify and calculate equal angles subtending the same arc.
• Use the centre/circumference theorem (the angle at the centre is double the angle at the circumference on the same arc) to find a missing angle.
• Use the cyclic quadrilateral theorem (opposite angles sum to 180 degrees) to find a missing angle.
• Solve multi-step problems that chain two circle theorems together, and explain which theorem justifies each step.