Basic Concept of A Circle
* The collection of all the points in a plane that are at equal distance from a given fixed point in the plane is called a circle.
* A line segment joining the centre of a circle with any point on its circumference is called the radius of a circle.
* A lines that joins two points on the circumference of the circle is a called a chord.
* A chord that passes through the centre of circle is called the diameter of a circle.
Diameter = 2 × Radius
* The part of the circumference of circle between two given points is called an arc.
* The region between two radii of the circle and any of the arcs between them is
called a sector.
Chords of A Circle
* The distance of a point from a line segment is equal to the length of the perpendicular drawn from the point to the line segment.
* The perpendicular from the centre of a circle to a chord bisects the chord.
* The line drawn from the centre of a circle to bisect a chord is perpendicular to chord.
* Equal chords of circle are equidistant from its centre.
* Chords equidistant from the centre of a circle are equal in length.
* Equal chords of a circle subtend equal angles at the centre.
* Chords that subtend equal angles at the centre of a circle are equal in length.
Arcs of A Circle
* Arcs of circle that superimpose each other completely are called congruent arcs.
* Chords corresponding to congruent arcs are equal.
* Corresponding arcs of a circle subtend equal angles at the centre.
* The angle subtended by an arc at a centre is double the angle subtended by the arc at any point on the remaining circle.
* Angles subtended by an arc at all points within the segment of the circle are equal.
* All angles formed in a semicircle are right angles.
Cyclic Quadrilateral
* Points that lie on the same circle are called concyclic points.
* Three points are concyclic if they are not collinear.
* If a line segment joining two points subtends equal angles at two other points on the same side of the line segment then all points are concyclic.
* A quadrilateral whose vertices lie on the circle is called a cyclic quadrilateral.
* In a cyclic quadrilateral, the sum of opposite angles is always equal to 180°.
* If the sum of opposite angles of a quadrilateral is 180°, then the quadrilateral is cyclic.