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Circle From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the shape and mathematical concept of circle. For list of topics related to circles, see List of circle topics. For all other uses, see Circle (disambiguation). Circle illustration showing a radius, a diameter, the center and the circumference Tycho crater, one of many examples of circles that arise in nature. NASA photoA circle is a simple shape of Euclidean geometry consisting of those points in a plane which are the same distance from a given point called the centre. The common distance of the points of a circle from its center is called its radius. Circles are simple closed curves which divide 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 (known as the perimeter) or to the whole figure including its interior. However, in strict technical usage, "circle" refers to the perimeter while the interior of the circle is called a disk. The circumference of a circle is the perimeter of the circle (especially when referring to its length). A circle is a special ellipse in which the two foci are coincident. Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone. Contents [hide] 1 Further terminology 2 History 3 Analytic results 3.1 Length of circumference 3.2 Area enclosed 3.3 Equation 3.4 Tangent lines 4 Properties 4.1 Chord properties 4.2 Sagitta properties 4.3 Tangent properties 4.4 Theorems 4.5 Inscribed angles 5 Apollonius circle 5.1 Cross-ratios 5.2 Generalized circles 6 See also 7 Notes This article is about the shape and mathematical concept of circle. For list of topics related to circles, see List of circle topics. For all other uses, see Circle (disambiguation). Circle illustration showing a radius, a diameter, the center and the circumference Tycho crater, one of many examples of circles that arise in nature. NASA photoA circle is a simple shape of Euclidean geometry consisting of those points in a plane which are the same distance from a given point called the centre. The common distance of the points of a circle from its center is called its radius. Circles are simple closed curves which divide 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 (known as the

perimeter) or to the whole figure including its interior. However, in strict technical usage, "circle" refers to the perimeter while the interior of the circle is called a disk. The circumference of a circle is the perimeter of the circle (especially when referring to its length). A circle is a special ellipse in which the two foci are coincident. Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone. Contents [hide] 1 Further terminology 2 History 3 Analytic results 3.1 Length of circumference 3.2 Area enclosed 3.3 Equation 3.4 Tangent lines 4 Properties 4.1 Chord properties 4.2 Sagitta properties 4.3 Tangent properties 4.4 Theorems 4.5 Inscribed angles 5 Apollonius circle 5.1 Cross-ratios 5.2 Generalized circles 6 See also 7 Notes 8 References 8.1 External links

[edit] Further terminology 8 References 8.1 External links