Circles

Circles

1. Chord

   • Any two points on a circle joined with line segment
   • Diameter
     • Chord passing through the centre of a circle
       • Longest Chord
     • d=2 * r=2r

2. Arc

   • Piece of circle between 2 points
     • Longer one : Major arc
     • Smaller one : Minor arc

3. Circle

   • Semicircle
     • Both regions are equal
     • Circular region is bisected by diameter
   • Circumference
     • Length of complete circle
       • =2*pi*r or pi*d

4. Segment

   • The region between a chord and either of its arc
     • Bigger one :Major segment
     • Smaller one : Minor segment

5. Collection of points in a plane, which are at fixed distance from a fixed point

   • Fixed
     • Point
       • Centre
     • Distance
       • Radius
   • Inside is
     • Interior
   • Outside is
     • Exterior
   • Circle and Interior
     • makes up circular region

6. Theorems

   • Equal chords of a circle subtend equal angles at the centre.
   • If the angles subtented by the chords of a circle at the 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 a circle to bisect a chord is perpendicular to the chord
   • There is one and only one circle passing through three given non-collinear points.
   • Chords equidistant from the centre of a circle are equal in length.
   • If a line segment joining two points subtends angles at two other points lying on the same side of the line containg the line segment, the four points lie on a circle (i.e. they are concyclic).
   • The sum of either pair of opposite angles of a cyclic quadrilateral is 180* .
   • If the sum of a pair of opposite angles of a quadrilateral is cyclic.
   • Angles in the same segment of a circle are equal
   • The angle subtented by an arc at the centre is double the angle subtended by it at any point on the remaining part of the cirale
   • Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).