The tangent and the radius
The angle between the tangent and the radius is 90º at the point of contact.
Two tangents from a point
For tangents to a circle, the distance from the point where they touch the circumference to the point where they meet is equal.
The perpendicular from the centre to a chord
The perpendicular from the centre of a circle to a chord bisects the chord.
The alternate segment theorem
The angle between a tangent and a chord is equal to the angle in the alternate segment.