# Circle A **circle** is a shape defined by the property that every point on the circle is a fixed distance from a specified centre point. A [[line segment]] from the centre to a point on the circle is called a **radius**, and its length is called **the radius** of the circle. A [[diameter]] of the circle is a [[line segment]] that joins two points on the circle which also passes through its centre. Its length is called **the diameter** of the circle. ## Circumference The [[perimeter]] of a circle is also called its **circumference**. A circle with radius $r$ has circumference $2 \pi r$. ## Area The [[area]] of a circle of radius $r$ is $\pi r^2$. ## Symmetry A circle has many [[symmetries]]: every rotation about its centre and every reflection in a line through its centre. Many results involving circles begin with the fact that any [[triangle]] with one [[vertex]] at the centre and the other vertices on the circle must be [[isosceles]] as two of its sides are radii of the circle and hence the same length. ## Related Shapes An **arc** of a circle is a connected part of the circle. A **semi-circle** is formed by taking an arc that consists of half the circle and joining its end points with a line segment, that must by necessity be a diameter. A **quarter-circle** is formed by taking an arc that consists of a quarter of the circle, and joining both its end points to the centre of the circle. A **sector** is formed by taking an arc of a circle and joining its end points to the centre of that circle. A **segment** is formed by taking an arc of a circle and joining its end points by a line segment. category: shape category: definition category: circle theorems [[!redirects area of a circle]] [[!redirects circle area]] [[!redirects circle areas]] [[!redirects circumference]] [[!redirects circle geometry]] [[!redirects circle theorems]] [[!redirects semi-circle]] [[!redirects circles]] [[!redirects radius]] [[!redirects radii]] [[!redirects centre]] [[!redirects quarter-circle]] [[!redirects sector]] [[!redirects segment]] [[!redirects arc]] [[!redirects arcs]]