A circle is set of all the points that are in the same plane and equidistant from a central point. The circle geometry involves calculation of circle’s radius, chord, diameter, secant, tangent, circumference, area, length of a circular arc, Area of circle sector, equation of circle using Cartesian polar and parametric coordinates.
Circle geometry also calculates symmetries of a circle, congruence and similarity of circle, angles at the centre and circumference and in a semicircle, cyclic quadrilateral and trigonometry. The circle geometry is a very useful tool.
Example 1: For a given circle with the radius 20 cm. Find the area and circumference of the circle.
Given: radius r = 20 cm.
The Formula for area of circle is area = π r * r = π r2
3.14 x 20 x 20 = 3.14 x 400 = 1256 cm2
Circumference of a circle = 2 π r
2 π x 20 = 2 x 3.14 x 20 = 125.6 cm.
Example 2: For a given circle with the radius 30 m. Find the sector area and length of the circular
arc if central angle is 30 degrees.
Given: radius r = 30 m
Central angle θ = 30 degrees
Area of sector = (θ/360) π r2
(30/360) x 3.14 x 30 x 30 = 1/120 x 3.14 x 900 = 23.55 m2
Length of circular arc = θ x (π/180) x r
30 x (3.14/180) x 30 = 5 x 3.14 = 15.7 m