# Circle

A **circle** is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. A circle is a round-shaped figure that has no corners or edges.

## Parts of Circle

- Annulus: a ring-shaped object, the region bounded by two concentric circles.
- Arc: any connected part of a circle. Specifying two end points of an arc and a centre allows for two arcs that together make up a full circle.
- Centre: the point equidistant from all points on the circle.
- Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments.
- Circumference: the length of one circuit along the circle, or the distance around the circle.
- Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; or the length of such a line segment. This is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord for a given circle, and its length is twice the length of a radius.
- Disc: the region of the plane bounded by a circle.
- Lens: the region common to (the intersection of) two overlapping discs.
- Passant: a coplanar straight line that has no point in common with the circle.
- Radius: a line segment joining the centre of a circle with any single point on the circle itself; or the length of such a segment, which is half (the length of) a diameter.
- Sector: a region bounded by two radii of equal length with a common centre and either of the two possible arcs, determined by this centre and the endpoints of the radii.
- Segment: a region bounded by a chord and one of the arcs connecting the chord's endpoints. The length of the chord imposes a lower boundary on the diameter of possible arcs. Sometimes the term
*segment*is used only for regions not containing the centre of the circle to which their arc belongs to. - Secant: an extended chord, a coplanar straight line, intersecting a circle in two points.
- Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as centre. In non-technical common usage it may mean the interior of the two-dimensional region bounded by a diameter and one of its arcs, that is technically called a half-disc. A half-disc is a special case of a segment, namely the largest one.
- Tangent: a coplanar straight line that has one single point in common with a circle ("touches the circle at this point").

## Semicircle:

Semi means half, so semicircle is half a circle. It is formed by cutting a whole circle along a line segment passing through the center of the circle. This line segment is called the diameter of the circle.

## Quarter Circle:

Quarter means one-fourth. So, a quarter circle is a quarter of a circle, formed by splitting a circle into 4 equal parts or a semicircle into 2 equal parts.

**Radius of a Circle: **A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle.

Radius = $\frac{Diameter}{2}$

**Diameter of a Circle:** A line segment passing through the center of a circle, and having its endpoints on the circle, is called the diameter of the circle.

**Diameter = 2 × radius**

**Chords of Circles: **A line segment with its endpoints lying on a circle is called the chord of the circle. The diameter of a circle is its largest chord.

**Arc of a Circle: **An arc is a part of the circle, with all its points on the circle. It is a curve that is a part of its circumference.

An arc that connects the endpoints of the diameter has a measure of 180° and it is called a semicircle.

An arc divides the circle into two parts. The smaller part is called the minor arc and the greater part is called the major arc.

**Secant of a Circle: **A secant is a line that intersects a circle at exactly two points.

**Tangent of a Circle: **A tangent is a line that intersects a circle at exactly one point.

**Segments of a Circle: **A chord of a circle divides the circular region into two parts. Each part is called the segment of the circle.

The segment containing the minor arc is called the minor segment and the segment containing the major arc is called the major segment.

**Sector of a Circle: **The sector of a circle is a part of the circle that is enclosed by two radii and an arc of the circle as a part of its boundary.

When two radii meet at the center of the circle to form the sector, it actually forms two sectors. A sector of a circle is called the minor sector if the minor arc of the circle is a part of its boundary. A sector is called the major sector if the major arc of the circle is a part of its boundary.

## Circle Formulas

**Area of a circle: **The area of a circle is the region enclosed inside the circle. The area of a circle depends on the length of its radius.

Area = $\pi $${r}^{2}$

**Circumference: **The distance around the circle is the circumference of the circle.

Circumference = 2$\pi $r