Mathematics - Circle properties and graphs 2F - 2I

Chord

Line going through inside of the circle

Arc

Any part of the circumference of a circle

Major arc

More than half of the circumference

Minor arc

Less than half of the circumference

Segment

Any parts of the circle separated by a chord not going through the centre.

Major segment

Segment more than half of the circle

Minor segment

Segment less than half of the circle

Chord theorem 1

Chords of equal length subtend equal angles at the centre of the circle

Chord theorem 2

Chords of equal length have the same minimum distance to the centre of the circle

Chord theorem 3

The perpendicularly from the centre of the circle to the chord bisects the chord and the angle at the centre subtended by the chord

Chord theorem 4

The perpendicular bisectors of every chord of a circle intersect at the centre of the circle

Circle theorem 1

The angle at the centre of a circle is twice the angle at a point on the circle subtended by the same angle

Circle theorem 2

For a semi-circle, the angle at the centre is 180, so the angle created at the point on the edge of the circle will be 90

Circle theorem 3

Angles at the circumference of a circle subtended by the same angle are equal

Circle theorem 4

Opposite angles in a quadrilateral with vertices on a circle are supplementary

Tangent

Line that touches the circle only once at a point of contact, perpendicular to radius.

Secant

Line that crosses circle twice

Alternate segment theorem

For any circle, the angle formed between the tangent and the chord through the point of contact of the tangent is equal to the angle formed by the chord in the alternate segment”.

Intersecting chord

Ac=bd

Intersecting secants at P

AP X BP = DP CP

Secant intersecting tangent

AP X BP =CP^2