Circles

Defination

The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.

Lines in a circle

Diametre

Chord

Radius

Secant

The line segment joining the centre of the circle to any of its point

The line segment from any one point on the circle to its opposite point

Line joining any 2 points on the circle

line cutting the circle on any two distinct points

Areas of circles

Segment

Sector

Arc

A piece of a circle between two points.

The region between a chord and either of its arcs is called a segment

The area between the arc and the centre is called sector.

Equal chords subtend equal angles at the centre and opposite.

The perpendicular from the centre of a circle to a chord bisects the chordand opposite.

There is one and only one circle passing through three given non-collinear points.

Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres) and opposite.

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Angles in the same segment of a circle are equal.

If a line segment joining two points subtends equal angles attwo other points lying on the same side of the line containing the line segment,the four points lie on a circle (i.e. they are concyclic) and opposite.

The sum of either pair of opposite angles of a cyclic quadrilateral is 180º and opposite.