Geometry

The angle at the center of the circle is double the angle at the circumference.

Angles in the same segment (from the same chord) are equal

The angle on the circumference in a semicircle is 90°.

Opposite angles in a cyclic quadrilateral add up to 180°

The alternate segment theorem

Tangents from a circle meeting at a external point are of equal length

Tangent is perpendicular to the radius.

The perpendicular bisector of a chord contains the center of the circle.

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add to 180°