- Opposite angles in a cyclic quadrilateral add to 180°
- The angle between a tangent and the radius is a right angle
- The perpendicular from the centre of the circle and a chord bisects the chord
A cyclic quadrilateral is a quadrilateral drawn inside a circle where all 4 points touch the circumference. Opposite angles in cyclic quadrilaterals add to 180°.
Angle Between tangent and radius:
The angle between the tangent of a circle and the radius is 90°.
This rule can be used to help prove the other tangent circle theorem, shown below.
Tangents which meet:
Tangents of a circle which meet at a point are the same length.
The tangents can start at any point on the circle. As long as they meet at a point, they will be equal in length from the point they touch circle to point they meet.
Draw radii from A and B, these are equal in length and meet the tangents at right angles.
This creates two triangles, OAC and OBC.
They share the line OC, both have a right angle and OA = OB
This means they are congruent (RHS)
Therefore, AC = BC
Therefore tangents which meet at a point are equal