Geometry of Circles
A circle is a simple shape of Euclidean geometry that is the set of all points in a plane that are at a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius. It can also be defined as the locus of a point equidistant from a fixed point.
A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is the former and the latter is called a disk.
A circle can be defined as the curve traced out by a point that moves so that its distance from a given point is constant.
A circle may also be defined as a special ellipse in which the two foci are coincident and the eccentricity is 0.
- Arc: any connected part of the circle.
- Centre: the point equidistant from the points on the circle.
- Chord: a line segment whose endpoints lie on the circle.
- Circular sector: a region bounded by two radii and an arc lying between the radii.
- Circular segment: a region, not containing the centre, bounded by a chord and an arc lying between the chord's endpoints.
- Circumference: the length of one circuit along the circle.
- Diameter: a line segment whose endpoints lie on the circle and which passes through the centre; or the length of such a line segment, which is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord, and it is twice the radius.
- Passant: a coplanar straight line that does not touch the circle.
- Radius: a line segment joining the centre of the circle to any point on the circle itself; or the length of such a segment, which is half a diameter.
- Secant: an extended chord, a coplanar straight line cutting the circle at two points.
- Semicircle: a region bounded by a diameter and an arc lying between the diameter's endpoints. It is a special case of a circular segment, namely the largest one.
- Tangent: a coplanar straight line that touches the circle at a single point.
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