Circle Theorems

Angle at circumference is half that at the centre

Angles in the same segment are equal

Opposite angles in a cyclic quadrilateral add to 180°

The angle at the circumference of a __**semicircle**__ is 90°

The angle between a tangent and a radius is 90°

The **perpendicular** from the centre of a circle to a **chord** **bisects** the chord.

Alternate Segment Theorem-The angle between a **tangent** and a **chord** is equal to the angle in the alternate segment.

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Tangents meeting at the same point are the same length