circle definition
15 Jan 2017
Definition: A circle is the locus of all points equidistant from a central point.
Definitions Related to Circles
diameter = 2 x radius of circle
arc: a curved line that is part of the circumference of a circle
chord: a line segment within a circle that touches 2 points on the circle.
circumference: the distance around the circle.
diameter: the longest distance from one end of a circle to the other.
origin: the center of the circle
pi (): A number, 3.141592..., equal to (the circumference) / (the diameter) of any circle.
radius: distance from center of circle to any point on it.
sector: is like a slice of pie (a circle wedge).
tangent of circle: a line perpendicular to the radius that touches ONLY one point on the 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 rif 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) PI r2if the angle
is in radians, then
area = (/2) r2Equation of Circle: (cartesian coordinates)
for a circle with center (j, k) and radius (r):
(x-j)2 + (y-k)2 = r2
Equation of Circle: (polar coordinates)
for a circle with center (0, 0): r(
) = radiusfor a circle with center with polar coordinates: (c,
) and radius a:r2 - 2cr cos(
- ) + c2 = a2Equation of a Circle: (parametric coordinates)
for a circle with origin (j, k) and radius r:
x(t) = r cos(t) + j y(t) = r sin(t) + k
