Circle

A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius.

Some Definitions:
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.
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 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.
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.
Sector: a region bounded by two radii and an arc lying between the radii.
Segment: a region, not containing the centre, bounded by a chord and an arc lying between the chord's endpoints.
Secant: an extended chord, a coplanar straight line cutting the circle at two points.
Semicircle: an arc that extends from one of a diameter's endpoints to the other. In non-technical common usage it may mean the diameter, arc, and its interior, a two dimensional region, 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 touches the circle at a single point.

Chord, secant, tangent, radius, and diameter Arc, sector, and segment

Formulas reated to circle:

Diameter = 2 x radius of circle

Circumference of Circle = PI x diameter = 2 PI x radius
where PI = = 3.141592...

Area of Circle:
area = PI r2

Length of a Circular Arc: (with central angle )
if the angle is in degrees, then length = x (PI/180) x r
if the angle is in radians, then length = r x
Area of Circle Sector: (with central angle )
if the angle is in degrees, then area = ( /360)x PI r2
if the angle is in radians, then area = (( /(2PI))x PI r2