Circle Theorems

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

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

An angle inscribed in a semicircle subtended by a diameter is always a right angle.

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

The opposite angles of a cyclic quadrilateral are supplementary.

Products of segments of intersecting secants or chords from a point are equal and equal the square of the tangent segment.

The tangent at any point on a circle is perpendicular to the radius drawn to the point of contact.

The lengths of two tangents drawn from an external point to a circle are equal and they subtend equal angles at the centre.

If a quadrilateral circumscribes a circle, the sums of the lengths of opposite pairs of sides are equal.

The angle between a tangent and a chord through the point of contact equals the angle subtended by the chord in the alternate segment.