A level History exam revision resources written by A level Examiners



Summary 7 major Circle Theorems

circle theorem 1 circle theorem 2 circle theorem 3

The angle subtended at the centre of a circle, by chord AB, is Twice the angle subtended at the circumference, by chord AB.

Angles subtended by an arc in the same segment of a circle are Equal.

Opposite angles of a cyclic quadrilateral add up to 180o

circle theorem 4 circle theorem 5 circle theorem 6

The angle in a semicircle is 90o, or
The angle on a diameter is 90o

The angle betweeen a tangent and a radius drawn to the point of contact is 90o

From any point outside a circle just two tangents to the circle may be drawn, and they are of equal length from the point outside the circle to the point of contact.

circle theorem 7

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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