Objective

To give a suggestive demonstration of the formula that the area of the circle is half the product of its circumference and radius.

Circle

It is the set of all points in a plane that are at a given distance from a given point, the centre.
A circle with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre (O) in magenta is below. [Refer Fig. 1]

                   Fig. 1: Circle

Related Terms

Center: A point inside the circle. All points on the circle are equidistant (same distance) from the center point.
Radius: The radius is the distance from the center to any point on the circle. It is half the diameter.
Chord: A segment of a straight line joining two points on a circle.
Diameter: The length of any chord passing through the center. It is twice the radius.
Circumference: The circumference is the perimeter of the circle. It is 2πr.
Area: Area of the region enclosed by the circle. It is π * r².

Properties of a circle

• The radius perpendicular to a chord bisects the chord.
• The diameter of a circle is the longest chord.
• The chords equidistant from the center are equal in length.
• A tangent to a circle is at right angles to the radius at the point of contact.
• Two tangents drawn to a circle from a point outside are equal in length.
• Circles that have equal radius are equal.