Lesson Basic formulas in a circle
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In this lesson we will be looking at the definition, different equations, area and circumference of the circle. <b>Circle</b> A circle is the set of all point in a plane that are at constant distance from a fixed point. Fixed point is called the "center of the circle" and the constant distance is called the " radius of the circle". {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, green(line( 2, 2,4.5,2)),red(circle( 2, 2,.2 )),circle( 2,2,2.5), locate(1.3,2.2, C), locate(3,1.9,r), locate(1.4,3.2,d),line(2,0,2,4))}}} In the figure above, C is the center of the circle. r is the radius of the circle. d is the diameter of the circle. It is twice of the radius. {{{d=2*r}}} <b>Circumference of the 'Circle'</b>: Perimeter(circumference) of the circle is given by the formula. {{{P=2*pi*r}}} Where: P is the circumference of the circle. r is the radius of the circle. <b>Area of the 'Circle'</b> Area of the circle is given by the formula. {{{A= pi*r^2}}} Where: A is the area of the circle. r is the radius of the circle. <b>Equation of the 'Circle'</b> In <b>"</b>x-y coordinate system<b>"</b> ('<A HREF=http://www.algebra.com/~pavlovd/wiki/Cartesian_coordinate_system>Cartesian coordinates</A>'), The equation of the circle with center <b>(a,b)</b> and radius <b>'r'</b> is {{{(x-a)^2+(y-b)^2=r^2}}} Solution of this equation gives the set of all points ({{{x}}},{{{y}}}) which are at constant distance <b>'r'</b> from a fixed point <b>(a,b)</b>. In <b>"Parametric form"</b>, the equation of the same circle is written as: {{{x=a+r*Sin(t)}}} {{{y=b+r*Cos(t)}}} Where: <b>(a,b)</b> is the center of the circle. <b>'r'</b> is the radius of the circle. 't' is the parameter which can take any real value between "{{{-infinity}}} to +{{{infinity}}}". Solution of this equation gives the set of all points ({{{x}}},{{{y}}}) which are at constant distance <b>'r'</b> from a fixed point <b>(a,b)</b>. In <b>"</b>Polar coordinate system<b>"</b>, the equation of the same circle is written as: The general equation for a circle with a center at ({{{r[o]}}}, {{{rho}}}) and radius <b>"R"</b> is {{{r^2-2*r*ro*Cos(theta - rho)+(ro)^2=R^2}}} Solution of this equation gives the set of all points (r,{{{theta}}}) which are at constant distance <b>'R'</b> from a fixed point <b>({{{r[o]}}}, {{{rho}}})</b>. For further reading on Circle refer to <A HREF=Circle.wikipedia>Wikipedia</A> on different Coordinate systems refer to <A HREF=http://www.algebra.com/algebra/homework/Length-and-distance/Different-type-of-coordinate-system.lesson> Lesson</A>