Geometry

Circle
	The figure on the left shows a circle of radius r with centre O. The two radii shown here OA and OC intersect the circle at points A and B defining a minor Arc-ABC, wherein B is the mid-point of the arc. It also defines a major Arc at the same time, which is Arc-ADC. The minor Arc-ABC subtends an angle y at the centre. The major Arc-ADC subtends an angle (360-y) at the centre. (360 is the angle subtended by the whole circle at the centre).
The ratio of circumference to diameter of a circle is defined as π (Greek alphabet, pronounced ‘pi’) which has a numerical value of  π = 22/7 = 3.14 (approx.) Area = (πd2)/4 (where d is the diameter, diameter = twice radius) or          = πr2 where r is the radius Perimeter or Circumference = 2πr                                                      = πd The length of an Arc is directly proportional to the angle subtended by the Arc at the centre of the circle. The length of arc can be obtained by multiplying the ratio of the angle subtended by the arc to the total angle subtended by the circle with the perimeter of the circle.  Ratio of the angle subtended by the minor Arc-ABC to the total angle subtended by the circle = (y/360) Length of minor Arc-ABC = (y/360)*(2πr) Length of major Arc-ADC = (360-y/360)*(2πr)
Sector
	Area enclosed by an arc and its radii is called a sector. The blue colour indicates the area of a sector. Like the length of an arc, the area of a sector is also directly proportional to the ratio of the angle subtended by the arc to the total angle subtended by the circle. The area of a sector is obtained by multiplying this ration with the area of the circle which it is part of. If the angle subtended by the minor Arc-ABC is y, then
Ratio of the angle subtended by the minor Arc-ABC to the total angle subtended by the circle = (y/360) Area of the sector AOC= (y/360)*(πr2)
Segment
	The area enclosed by a chord and an arc is termed as a segment. In the figure on the left area shaded in blue is the segment formed by chord AC and Arc-ABC. A chord is a line segment joining any two points on a circle. The diameter is the largest chord a circle can have. In the figure on the left, ABC is the minor segment and ADC is the major segment.
If the radii OA and OC have a value r and the Arc-ABC subtends an angle y at the centre O, then the area of the segment ABC can be obtained from the relation given below:   Area of a segment = (r2/2)[{(π/180)*y}-Sin y]