IIT JEE Circles

Hello sir I am here as I want to get important Formulas of Circles Topics of the IIT JEE Exam so will you please provide me the Formulas??

[sumit]

Circle holds a high pedestal in the entire Syllabus of Co-ordinate Geometry in Mathematics. The preliminary knowledge of the concept of Straight Lines is a prerequisite to study Circles.

The general equation of a circle in Cartesian coordinates with centre at (a, b) and radius r is given by



If the center is at (0, 0) then the equation becomes




In parametric form it may be represented as







where t is a parameter ranging between 0 to 2π.



Important terms and formulae related to circles:

-Length of circumference in a circle is given by 2πr, where r is the radius.

-The diameter is the longest chord of the circle.

-Area of a circle is given by πr2.

-The circle which is centered at the origin with radius 1 is called the unit circle.

-A line segment whose end points lie on a circle is defined as a chord.

-A line that cuts a circle at two distinct points is called a secant.

-Chords are equidistant from the center of a circle if and only if they are equal in length.

-Equal chords of a circle subtend equal angles at the center


Representation of various terms related to circles

-An arc is a section of the circumference of a circle.

-A sector is an area of a circle bounded by 2 radii.

-A quadrant is one-quarter of a circle.

-A segment of a circle is the part bounded by a chord and the circumference.

-Equal arcs of a circle subtend equal angles at the center.

-An angle in a semi-circle is a right angle.