Circle Theorems

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Last updated 6:21 PM on 6/29/26
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8 Terms

1
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Angle at the centre

The angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any point on the circumference.

2
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Angles in the same segment

Angles subtended by the same arc at the circumference are equal.

3
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Cyclic quadrilateral

The opposite angles of a cyclic quadrilateral sum to 180° (are supplementary).

4
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Tangent and radius

A tangent is perpendicular to the radius at the point of contact.

5
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Two tangents meeting

Tangents drawn from an external point to a circle are equal in length.

6
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Alternate segment

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.

7
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Perpendicular bisector

A perpendicular line drawn from the centre of a circle to a chord bisects the chord.

8
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Angle in a semicircle

The angle subtended by a diameter at the circumference is a right angle