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Circle Theorems

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Examples, solutions, and videos to help GCSE Maths students learn the circle theorems.

Circle Theorems 1
The angle at the centre is twice the angle at the edge for configurations with intersecting lines.
Circle Theorem 2 (angle is a semi circle)
The angle in a semi-circle is always 90 degrees.

Circle Theorems 3 (Angles in the same arc)
Angles in the same segment are equal. (Bow theorem)
Circle Theorems 4 (cyclic quads)
Opposite angles in a cyclic quadrilateral add up to 180 degrees The Alternate Segment Theorem
The angle between a tangent and a chord is equal to the angle in the alternate segment.

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