Dave's Math Tables: Circles |
a circle |
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 r^{^2}
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 r^{2}
if the angle is in radians, then
area = (/2)x PI r^{2}
Equation of Circle: (cartesian coordinates)
for a circle with center (j, k) and radius (r):
(x-j)^{^2} + (y-k)^{^2} = r^{^2}
Equation of Circle: (polar coordinates)
for a circle with center (0, 0):
r() = radius
for a circle with center with polar coordinates: (c, ) and radius a:
r^{2} - 2cr cos( - ) + c^{2} = a^{2}
Equation 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