Circle theorems practice questions

Key circle theorems include: the angle at the centre is twice the angle at the circumference on the same arc, the angle in a semicircle is 90 degrees, and opposite angles in a cyclic quadrilateral add to 180 degrees. GCSE marks require naming the theorem, not just the calculation.

Circle theorems are a GCSE Higher topic where marks come from naming the rule as well as calculating the angle. Examiners expect the reason written alongside the working.

The method, step by step

1. Angle at the centre. The angle at the centre is twice the angle at the circumference on the same arc.
2. Angle in a semicircle. An angle drawn in a semicircle is always 90°.
3. Same segment. Angles in the same segment are equal.
4. Cyclic quadrilateral. Opposite angles in a cyclic quadrilateral add to 180°.
5. Tangent and radius. A tangent meets a radius at 90°.

Worked example

Common mistakes

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