Topics
Number Systems
Real Numbers
Algebra
Pair of Linear Equations in Two Variables
 Linear Equations in Two Variables
 Graphical Method of Solution of a Pair of Linear Equations
 Substitution Method
 Elimination Method
 Cross  Multiplication Method
 Equations Reducible to a Pair of Linear Equations in Two Variables
 Consistency of Pair of Linear Equations
 Inconsistency of Pair of Linear Equations
 Algebraic Conditions for Number of Solutions
 Simple Situational Problems
 Pair of Linear Equations in Two Variables
 Relation Between Coefficient
Arithmetic Progressions
Quadratic Equations
 Quadratic Equations
 Solutions of Quadratic Equations by Factorization
 Solutions of Quadratic Equations by Completing the Square
 Nature of Roots
 Relationship Between Discriminant and Nature of Roots
 Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
 Quadratic Equations Examples and Solutions
Polynomials
Geometry
Circles
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
 Tangent to a Circle
 Number of Tangents from a Point on a Circle
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Triangles
 Similar Figures
 Similarity of Triangles
 Basic Proportionality Theorem Or Thales Theorem
 Criteria for Similarity of Triangles
 Areas of Similar Triangles
 Pythagoras Theorem
 Similarity Triangle Theorem
 Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
 Triangles Examples and Solutions
 Angle Bisector
 Similarity
 Ratio of Sides of Triangle
Constructions
Trigonometry
Heights and Distances
Trigonometric Identities
Introduction to Trigonometry
Statistics and Probability
Probability
Statistics
Coordinate Geometry
Lines (In Twodimensions)
Mensuration
Areas Related to Circles
Surface Areas and Volumes
definition
 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.
 Centre of a circle: The fixed point is called the centre of the circle.
 Radius of a circle: The line segment joining the centre and any point on the circle is called the radius of the circle.
 Circumference of a circle: The Perimeter of the circle is called the circumference.
 Chord of a circle: The line segment, joining any two points on the circumference of the circle, is called a chord.
 Sector of a circle: A sector is a region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.
 Segment of a circle: A segment of a circle is a region in the interior of the circle enclosed by an arc and a chord.
 Semicircle: A semicircle is half of a circle, with the endpoints of diameter as part of the boundary.
notes
Circles:

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 line segment joining the centre and any point on the circle is also called a radius of the circle. That is, ‘radius’ is used in two senses in the sense of a line segment and also in the sense of its length. 
The Perimeter of the circle is called the circumference.

The line segment, joining any two points on the circumference of the circle, is called a chord.

A chord, which passes through the centre of the circle is called the diameter and is the largest chord of the circle which is equal to two times the radius.
 A sector is a region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.

A segment of a circle is a region in the interior of the circle enclosed by an arc and a chord.

A diameter of a circle divides it into two equal parts; each part is a semicircle. A semicircle is half of a circle, with the endpoints of diameter as part of the boundary.

A circle divides the plane on which it lies into three parts.
They are:
(i) inside the circle, which is also called the interior of the circle;
(ii) the circle and
(iii) outside the circle, which is also called the exterior of the circle, which is also called the exterior of the circle. The circle and its interior make up the circular region.