Circles and its Related Terms by andyikumar

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									                      Circles and its Related Terms

Circles and its Related Terms
A circle is a simple shape of Euclidean geometry that is the set of points in the plane that are equidistant
from a given point, the centre. The distance between any of the points and the centre is called the
radius. 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. Circles are conic sections attained
when a right circular cone is intersected by a plane perpendicular to the axis of the cone.

Its Related Terms

Chord: a line segment whose endpoints lie on the circle.
Diameter: the longest chord, a line segment whose endpoints lie on the circle and which passes through
the centre; or the length of such a segment, which is the largest distance between any two points on the
circle.


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Radius: a line segment joining the center of the circle to any point on the circle itself; or the length of
such a segment, which is half a diameter.
Circumference: the length of one circuit along the circle itself.
Tangent: a straight line that touches the circle at a single point.
Secant: an extended chord, a straight line cutting the circle at two points.
Arc: any connected part of the circle's circumference.
Sector: a region bounded by two radii and an arc lying between the radii.
Segment: a region bounded by a chord and an arc lying between the chord's endpoints.


Properties :- The circle is the shape with the largest area for a given length of perimeter. (See
Isoperimetric inequality.) The circle is a highly symmetric shape: every line through the centre forms a
line of reflection symmetry and it has rotational symmetry around the centre for every angle. Its
symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T. All
circles are similar.
A circle's circumference and radius are proportional.
The area enclosed and the square of its radius are proportional.
The constants of proportionality are 2π and π, respectively.
The circle which is centred at the origin with radius 1 is called the unit circle.
Thought of as a great circle of the unit sphere, it becomes the Riemannian circle.
Through any three points, not all on the same line, there lies a unique circle. In Cartesian coordinates, it
is possible to give explicit formulae for the coordinates of the centre of the circle and the radius in
terms of the coordinates of the three given points. See circumcircle.




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