Everything about Circle totally explained
Circles are simple
shapes of
Euclidean geometry. A circle consists of those
points in a
plane which are at a constant
distance, called the
radius, from a fixed point, called the
center. A circle with center
A is sometimes denoted by the symbol .
A
chord of a circle is a line segment whose both endpoints lie on the circle. A
diameter is a chord passing through the center. The length of a diameter is twice the radius. A diameter is the largest chord in a circle.
Circles are simple closed
curves which divide the plane into an interior and an exterior. The
circumference of a circle is the perimeter of the circle, and the interior of the circle is called a
disk. An
arc is any
connected part of a circle.
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.
Analytic results
In an
x-
y Cartesian coordinate system, the circle with center (
a,
b) and radius
r is the set of all points (
x,
y) such that
»
The
equation of the circle follows from the
Pythagorean theorem applied to any point on the circle. If the circle is centred at the origin (0, 0), then this
formula can be simplified to
»
When expressed in
parametric equations, (
x,
y) can be written using the
trigonometric functions sine and cosine as
»
where
t is a
parametric variable, understood as many the angle the ray to (
x,
y) makes with the
x-axis. Alternatively, in
stereographic coordinates, the circle has a parametrization
» (1)
is not a circle, but rather a line.
Thus, if
A,
B, and
C are given distinct points in the plane, then the locus of points
P satisfying (1) is called a
generalized circle. It may either be a true circle or a line.
Further Information
Get more info on 'Circle'.
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