The angle in a semi-circle is a right angle / 90o
The perpendicular from a chord to the centre of the circle bisects the chord
The angle between a tangent and a chord is equal to the angle in the alternate segment
Alternate segment theorem
The angle at the centre of the circle is twice the angle on the circumference
Angles in the same segment are equal
Opposite angles of a cyclic quadrilateral add up to 180o
Tangent meets radius at 90o
2 tangents from the same point are equal = isosceles triangle
Angles at the base of an isosceles triangle are equal