Theorems of circle

Theorem 1

There is a unique circle passing through three non collinear points

Theorem 2

Equal chords of a circle subtend equal angles at the centre of the circle.

Theorem 3

Chords of a circle that subtend equal angles at the centre are equal

Theorem 4

The line joining the centre of a circle and the midpoint of a chord of the circle is perpendicular to the chord.

Theorem 5

The perpendicular from the centre of a circle to a chord of the circle bisects the chord

Theorem 6

Chords of a circle having the same length are all at the same distance from the centre.

Theorem 7

Chords of a circle that are equidistant from the centre have equal length

Theorem 8

If ab is bigger than de then the distance from C to ab is less than the distance from C to de

Theorem 9

The annual subtended by an Arc at the centre of the circle is double the angle subtended by the arc at any point on the circle outside the circle.

Theorem 10

If a line segment AB joining 2 pointsA,B subtend equal angle at 2 other points C, D that lie on the same side of AB then the four points lie on the circle .

Theorem 11

The sum of two opposite angles of a cyclic quadrilateral is 180° .

Theorem 12

If two opposite angles of a quadrilateral add up to 180°, they are concyclic.