Circles Formulaes

Introduction to circles: A circle is geometrical figure consisting of all those points in a plane which are at a given distance from a fixed point in the same plane .The fixed point is called the centre of the circle and the constant distance id known as its radius.A circle with centre O and radius r is generally denoted by C(o, r) .
Perimeter of a circle: The perimeter of a circle is called its circumference. The length of the thread that winds around the circle exactly one , gives the circumference  or perimeter of a circle .The ratio of  a perimeter of a  circle and its diameter is always constant .The circumference or perimeter of a circle C of radius r is given by C= 2(pi)r..If d denotes the diameter of the circle .Then D= 2r, Therefore C =( pi) d

Tangent circles: Tangent: tangent of a circle is a line that intersects the circle in exactly one point. The point is called the point of contact of the tangent and the line is said to touch the circle at this point. The word tangent is originated from the Latin word TANGERE which means ‘to touch’.

The point of contact is the only point which is common to the tangent and the circle and every other point on the tangent lies outside the circle. Thus, of all the points on a tangent to a circle, the point of contact is nearest to the centre of the circle.
Tangent from a point to a circle: No tangent can be drawn to a circle from a point lying inside it. One and only one tangent can be drawn to a circle at a point on the circle. Two tangents can be drawn to a circle from a point lying outside it.

Circle formulas
For a circle of a radius r , we have
(i) Circumference = 2 theta
(ii) Area = theta2
(iii) Area of semicircle =theta2/2
(iv) Area of quadrant = theta2/4

2)  If R and r are the radii of two concentric circles such that R>r then, Area enclosed by the two circles = theta2 - theta2 = p(R2-r2).

3) If a sector of a circle of radius r contains an angle theta°. Then,
(i) Length of the arc of sector = theta/360 x 2theta = theta/360 x (circumference of the circle)
(ii) Perimeter of the sector = 2r + theta/360 x 2theta
(iii) Area of the sector = theta/360 x theta2 = theta/360 x (Area of the circle)
(iv)Area of segment = Area of corresponding sector – Area of corresponding triangle =theta/360 xtheta2-r2sin theta/2 costheta/2