Area of Circles and Ellipse

  • The Circle and Parts of a Circle

    The Circle: A circle is a plane curve consisting of all points that have the same distance from a fixed point called center the common distance of the points on the curve from the center is called the radius. The region bounded by the circle is also often referred to as a circle (as when […]

  • Properties of the Circle

    In geometry, a large number of facts about circles and their relations to straight lines, angles and polygons can be proved. These facts are called the properties of the circle. Circles having equal radii are congruent. Circles having different radii are similar. The central angle which intercept an arc double of any inscribed angle that […]

  • Area of a Circle

    Consider the first figure and suppose that one semi-circle is cut form the centre nearly to the circumference in each direction. Then the semi-circle is spread out as in second figure. The length is the length half circumference of the circle. Suppose that the other half of the circle is cut in the same way […]

  • Relation Between the Circumference and Diameter

    It we measure the circumference and diameter of various circles; we will find that the ration of circumference and their corresponding diameters, is always constant. This constant ratio is denoted by Greek letter . The value of is 22/7or 3.1415.                            Or                                                          Or          (, being radius) Example: The sum […]

  • Area of a Circular Ring or Annulus

    Annulus: A circular ring (annulus) is plane figure bounded by the circumference of two concentric circles of two different radii. The area of a circular ring is found by subtraction the area of small circle from that of the large circle. The examples of annulus are the area of a washer and the area of […]

  • Area of a Sector

    A sector is a portion of a circle bounded by two radii and the arc joining their extremities. It is thus a form of triangle with a covered base. In the figure the portion is a sector. Arc is called the arc of the sector and is called the angle of the sector. The area […]

  • Area of a Segment

    A segment is a portion of a circle which cut off by a straight line not passing through the centre. The segment, smaller than the semi-circle is called the minor segment and the segment larger than the semi-circle is called the major segment. (a) Area of the minor segment when angle and radius are given: […]

  • Area of an Ellipse

    Ellipse: An ellipse is a curved line such the sum of the distance of any point in it from two fixed points is constant. In the figure and are the two fixed points. The fixed points are called foci. The point is the center of the ellipse. is the major axis and is the minor […]

  • Perimeter of an Ellipse

    The perimeter or circumference of an ellipse is difficult to determine accurately. Various approximation formulas are given for finding the perimeter of an ellipse. (a) If the ellipse is very nearly of the shape of a circle (i.e., if the major and minor axes are nearly equal), then perimeter is given by (1)             Where […]