Inscribed angle is an angle created from any 2 points on the circumference of a circle meeting on a 3rd point on the circumference.  The central angle is an angle created from any 2 points on the circumference of a circle meeting at the centre of the circle.

The inscribed angle is always half the size of the central angle.

An angle inscribed in a semicircle is always a right angle.

Angles in the same segment (same 2 starting points on the circumference) are always equal.

A cyclic quadrilateral is a quadrilateral (4-sided shape) whose vertices all touch the circumference of a circle.

Opposite angles in a cyclic quadrilateral add up to 180 degrees or is supplementary.

The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

A chord is a straight line from one point on the circumference of a circle to another.

If a chord is bisected (split evenly) by the radius of a circle, then both sides of the chord are equal in length.

It also forms a 90 degree angle between the chord and the radius.

Chords that are equal in length are equidistant (same distance) from the circle centre.

When two chords intersect inside a circle, this divides each chord into two line segments in which the product of the lengths of the line segments for both chords is the same.

A secant is a line that cuts a circle twice.

A tangent is a line that touches the circumference of a circle at one point only.

A tangent that touches a radius of the circle always creates a 90 degree angle (right angle).

If two tangents intersect outside of a circle, the distances along the tangent from the intersection to the circumference of the circle are equal.

If two secants intersect outside a circle, the product of the entire secant length by the external secant length will be the same.

If a tangent and a secant intersect outside a circle, the product of the entire secant length by the external secant length will be equal to the square of the tangent length.