## Objective:

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

### Definition:

**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:

### 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 .

**Area:** Area of the region enclosed by the circle. It is .

## Properties of a circle:

- The radius perpendicular to a chord bisects the chord.
- The diameter of a circle is the longest chord.