# Parts of a Circle

By the end of this lesson, you will be able to

- define circle.
- describe different parts of a circle.
- derive the formula for area of a circle.
- evaluate the area of a circle.
- calculate the perimeter of a circle.

## Circle

A circle is a plane closed shape formed by the set of all points that are equidistant from a fixed point.

Different parts of circle

Equidistant means the distant of all points from a given point is constant. The fixed point is called the center of the circle. And the distance between one of the points on the boundary of the circle and the center is called the radius.

Therefore, a circle is uniformly round curved shape in plane geometry.

Click on any circle to enlarge it and see the change.

### Center of a circle

Center of a circle is the point equidistant from any point on its boundary.

### Radius of a circle

The radius of a circle is the length of a line segment between center and any point on its boundary.

### Diameter of a circle

A diameter of a circle is a line segment passing through the center and whose endpoints lie on the boundary of that circle. Its length is twice the radius. The center is the midpoint of diameter of a circle. Again a diameter is a particular chord. That is a diameter the longest chord passes through the center.

### Area of Circle

Area of a circle on a plane means how much surface it contains. It is the π times the square of the radius of the circle. π is the ratio of circumference to its diameter of a circle. If the diameter of a circle is 7, its circumference is 22. So, circumference : radius = 22:7. Hence, π = 227. If the radius of circle is r, the area of circle is πr^{2} square unit.

#### Area of Circle Calculator

If the radius and area of a circle r and A respectively,

A = πr^{2} square unit

### Chord of a circle

A chord of a circle is a line segment joining two points on the circle.

### Tangent of a circle

A tangent of a circle is a straight line touches the circle at a single point. A tangent at a point of a circle is perpendicular to the radius passes through the point.

### Circumference of a circle

The distance around the boundary of a circle is the circumference of that circle. It is the π times the diameter of the circle. That is, one can determine the circumference of a circle by multiplying the diameter with π. Therefore, if the radius of a circle is r, its circumference is 2πr.

#### Circumference calcualator

If the radius and circumference of a circle are r and C respectively,

C = 2πr unit

### Secant of a circle

A secant of a circle is a straight line that intersects two points on the circle. A secant is an extended chord meets the circle at two points.

### Arc of a circle

An arc of a circle is a portion or segment of circumference of the circle. A line segment whose endpoints are the endpoints of an arc of a circle is a chord.

### Semicircular Arc of a circle

An arc of a circle is said to be semicircular arc if the arc length is exactly half the circumference.

### Segment of a circle

A segment of a circle is a region of a disk enclosed by a chord and an arc.

### Sector of a circle

A sector of a circle is a region of a disk enclosed by two radii and an arc.

Different parts and portion of area