CIRCLE
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. The fixed point is called the centre of the circle.
The fixed distance is called the radius of the circle.
The chord that passes through the centre and joins two points on the circle is called the diameter.
Circumference: The length of the complete circle is called its circumference.
Segment: The region between a chord and either of its arcs is called a segment.
Sector: The region between an arc and the two radii joining the centre to the end points of the arc is called a sector.
THEOREMS:
- Equal chords of a circle subtend equal angles at the centre.
- If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
- The perpendicular from the centre of a circle to a chord bisects the chord.
- The line drawn through the centre of circle to bisect a chord is perpendicular to the chord.
- There is only one circle passing through three given non-collinear points.
- Equal chords of a circle are equidistant from the centre.
- Chords equidistant from the centre of a circle are equal in length.
- 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 segments of a circle are equal.
- If a line segment joining two points subtends equal angles at other points lying on the same side of the line containing the line segment, the four points lie on a circle.
- The sum of either pair of opposite angles of a cyclic quadrilateral is 180o