Circles

The angle subtended by an arc

The angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining part of the circle. If ∠POQ is

All angles subtended by the same

All angles subtended by the same arc on the same side of the chord are equal. For example, if points R and S are on the same side of chord PQ, then ∠P

Any angle subtended by a diameter

Any angle subtended by a diameter (semicircle) at any point on the circle is always 90°. This is because the central angle for a diameter is 180°, so

In a cyclic quadrilateral (quadrilateral inscribed

In a cyclic quadrilateral (quadrilateral inscribed in a circle), opposite angles are supplementary (sum to 180°). Also, the exterior angle equals the

A tangent to a circle

A tangent to a circle is perpendicular to the radius at the point of contact. From any external point, exactly two tangents can be drawn to a circle,