Circle is a round plane figure whose boundary consists of points equidistant from center such as a curved upper tier of seats in a theater or a group of people forming a circle. Areas related to circle is defined as the total area enclosed by the circumference of a circle. Areas related to circles gives the measurement of surface of a circle.
Areas related to circles is given by:
A = ∏ r^{2},
Here 'r' is radius of circle and value of '∏' is 3.14 (approx value).
Some terms of areas related to circles are:
Radius: It is a straight line from the center of a circle or a radial line from the focus to any point of a curve. It is also known as a specified distance from a center in all direction. It is denoted by ‘r’.
Circumference: It is defined as the enclosing boundary of a circle.
Diameter: It is a straight line passing from side to side through the center of a circle.
Tangent: It is a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.
Origin: it is a fixed point from which the coordinates are measured.
Pi (∏): The approximate value of 'pi' is given as 3.14.
Circumference of circle is given by:
C = 2 ∏ r,
Here '∏' and 'r' are same as defined above.
Areas related to circles in terms of diameter is given as:
A = ∏ d^{2} / 4,
Here 'd' is the diameter of a circle.
In Cartesian coordinates the equation of a circle is written as:
(x – a)^{2} + (y – b)^{2} = r^{2},
Here 'r' is the radius of circle, (x , y) is the set of points in a circle and (a, b) is the center coordinates. Suppose if (a, b) is centered at origin then the above equation is written as:
x^{2} + y^{2} = r^{2},
Equation of circle in parametric coordinates is given by:
x (t) = r cos (t) + x_{1}, y(t) = r sin (t) + y_{1},
Properties of areas related to circles:
1. Area of a circle is directly proportional to square of radius and diameter of circle.
2. All circles are in same figure.