Circle Theorems

The circle theorems and rules needed for GCSE maths

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Angle subtended at Centre of Circle

Angle at the centre (

The angle subtended at the centre of a circle (a) is twice the angle subtended at the circumference (b) within the same segment

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Angles subtended by a Chord in the same Segment

Angles subtended on the same arc (

Angles subtended by a chord in the same segment of the circle are equal

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Angles in a Cyclic Quadrilateral


Opposite angles of a cyclic quadrilateral add up to 180 degrees -         A+C = 180 degrees - B+D = 180 degrees

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Angle in a Semi-circle

angle in a semi-circle (

The angle in a semi-circle is 90 degrees

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Perpendicular Bisector of a Chord


The perpendicular bisector of any chord passes through the centre of the circle (0)

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Two Tangents to a Circle


From any point outside a circle, two tangents to the circle can be drawn and they are of equal length: PA = PB

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Angle between Tangent and Radius


The angle between a tangent and the radius drawn to the point of contact is 90 degrees

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Alternate Segment Theorem


The angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment

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This is really useful!

Hannah Gluyas


this is very useful :)



exactly what i was looking for.

thanks x



This was very useful, thankyou :)

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