User:Alcsai/Circle

=Circle=

Definition
A Circle is a the locus of points on a plane which moves such that its distance from fixed point remains constant. The fixed pint is called "Center" and the constant distance is called the "Radius" of the Circle.


 * 1) A Circle having radius 1 Unit is called "Unit Circle".
 * 2) Two or more Circles are said to be "Concentric Circles" if their Centers Coincides each other.
 * 3) Circles having Equal radii are called "Congruent Circles".
 * 4) Circle having radius zero is called a "Point Circle".

Basic Theorems

 * 1) There exist only one circle passing through three non-collinear points.
 * 2) If two circles intersects at two points then the line joining centers is perpendicular bisector of the common chord.
 * 3) The perpendicular from center of a circle to a chord bisects the chord.
 * 4) Perpendicular bisectors of two chords intersects at its center.
 * 5) Equal chords of a circle are at equidistant from the center.
 * 6) If two equal chords are drawn from a point, then the center of the circle lies on the angular bisector of these chords.
 * 7) Of any two chords of a circle larger will be near to the center.
 * 8) Angle subtended by an arc at the center is double the angle subtended by it at any point on alternate segment.
 * 9) Angles in the same segment are equal.
 * 10) The angle in semicircle is a right angle.