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 (http://www.mathsrevision.net/gcse/Circle4.gif)

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 (http://www.mathsrevision.net/gcse/Circle1.gif)

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

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Angles in a Cyclic Quadrilateral

(http://www.mathsteacher.com.au/year10/ch06_geometry/10_cyclic_quadrilaterals/Image4172.gif)

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 (http://www.mathsrevision.net/gcse/Circle9.gif)

The angle in a semi-circle is 90 degrees

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Perpendicular Bisector of a Chord

(http://www.onlinemathlearning.com/image-files/chords-circle_clip_image002.gif)

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

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Two Tangents to a Circle

(http://literacy.calumet.purdue.edu/student/bakerl3/tangent_tangent.gif)

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

(http://www.pgce.soton.ac.uk/ict/ma/circle/5.gif)

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

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Alternate Segment Theorem

(http://www.mathsrevision.net/gcse/Circle5.gif)

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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Comments

Amina

This is really useful!

Hannah Gluyas

this is very useful :)

Emily

exactly what i was looking for.

thanks x

RiverSong

This was very useful, thankyou :)

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