Circle

A circle is a two-dimensional geometric shape. It consists of all points on a plane that are equidistant from a single point called the center. This constant distance is called the radius.

The circle is one of the most fundamental shapes in geometry. It is used to measure circumference, calculate area, and define angles. It also underlies many engineering applications, such as wheels and gears.

Key Components

The center is the point from which distance is measured. The radius is the line segment from the center to the edge of the circle. The diameter is a line passing through the center connecting two points on the edge; it equals twice the radius. The length of the boundary of a circle is called the circumference.

Measurement

The circumference is calculated using a formula involving pi (π), the ratio between the circumference and the diameter. The circumference is 2πr, while the area is πr². Here r is the radius. Pi is not a rational number that can be expressed as a simple fraction; its approximate value is 3.14159.

Related Lines

A line that intersects a circle at two points is called a secant, while a line that touches the circle at only one point is called a tangent. A tangent is always perpendicular to the radius at the point of contact. A line inside the circle connecting two points on the edge is called a chord; the diameter is the longest chord.

Applications

Circles are used in mapping, calculating circumferences, and describing rotational motion in physics. They also appear in optical and imaging systems, where light rays are measured in a circular pattern.