Circle Properties in Geometry

A circle is a fundamental shape in geometry. It is defined as a set of all points in a plane that are equidistant from a given point, known as the center. Below are some key properties of a circle.

Key Properties of a Circle

  • Radius: The distance from the center to any point on the circle.
  • Diameter: The distance across the circle through the center, which is twice the radius.
  • Chord: A line segment whose endpoints are on the circle.
  • Tangent: A line that touches the circle at exactly one point.
  • Secant: A line that intersects the circle at two points.

Circle Formulas

Here are some important formulas related to circles:

  • Area of a Circle: ( A = \pi r^2 )
  • Circumference of a Circle: ( C = 2\pi r )
  • Area of a Sector: ( A = \frac{\theta}{360} \times \pi r^2 )
  • Length of an Arc: ( L = \frac{\theta}{360} \times 2\pi r )

Example

If the radius of a circle is 5 units, the area and circumference would be:

  • Area: ( 25\pi ) square units
  • Circumference: ( 10\pi ) units

Circle Diagram

For more information on circle properties and geometry, you can visit our Geometry Introduction.