Circles

Definition: A circle is the locus of all points equidistant from a central point.




Definitions Related to Circles

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 (π): 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.


Diameter = 2 x radius of circle

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

Area of Circle:

area = PI r²

Length of a Circular Arc: (with central angle ø )
if the angle ø is in degrees, then length = ø x (PI/180) x r
if the angle ø is in radians, then length = r x ø

Area of Circle Sector: (with central angle ø )
if the angle ø is in degrees, then area = (ø/360)x PI r²
if the angle ø is in radians, then area = ((Ø/(2PI))x PI r²

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(Ø) = radius

for a circle with center with polar coordinates: (c, ) and radius a:
r²- 2cr cos(Ø-a ) + c² = a²
Equation of 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