Circle Geometry

Circle Geometry A circle is set of all the points that are in the same plane and equidistant from a central point. The circlegeometry involves calculation of circles radius, chord, diameter, secant, tangent, circumference, area, lengthof 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 thecentre and circumference and in a semicircle, cyclic quadrilateral and trigonometry. The circle geometry is avery useful tool. Example 1: For a given circle with the radius 20 cm. Find the area and circumference of the circle. Solution: Given: radius r = 20 cm. The Formula for area of circle is area = r * r = r2 3.14 x 20 x 20 = 3.14 x 400 = 1256 cm2 Circumference of a circle = 2 r 2 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. Solution: Given: radius r = 30 m Central angle = 30 degrees Area of sector = (/360) r2 (30/360) x 3.14 x 30 x 30 = 1/120 x 3.14 x 900 = 23.55 m2 Length of circular arc = x (/180) x r 30 x (3.14/180) x 30 = 5 x 3.14 = 15.7 m