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terms associated with a circle
Terms associated with a circle
The set of all points in a plane at a given distance r, called the radius, from a fixed point, called the center. A circle is a simple closed curve that divides the plane into an interior and exterior. It has a perimeter, called a circumference, of length 2πr, and encloses an area of πr 2.

In coordinate geometry a circle with center (x0, y0) and radius r is the set of all points (x, y) such that:

(x - x0)2 + (y - y0)2 = r 2.

"Circle" comes from the Latin circus, which refers to a large round or rounded oblong enclosure in which the famous Roman chariot races were held.

A line cutting a circle in two places is called a secant. The segment of a secant bound by the circle is called a chord, and the longest chord is that which passes through the center and is known as a diameter. The ratio of the circumference to the diameter is π. The length of a circle between two radii is called an arc; the ratio between the length of an arc and the radius defines the angle between two radii in radians. The area bounded by two radii and an arc is known as a sector. A line touching a circle in one place is called a tangent. Tangent lines are perpendicular to radii.

In affine geometry all circles and ellipses become congruent, and in projective geometry the other conic sections join them. A circle is a conic section with eccentricity zero. In topology all simple closed curves are homeomorphic to circles, and the word circle is often applied to them as a result. The three-dimensional analog of the circle is the sphere, and the four-dimensional analog is the hypersphere.

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