Circles

circle picture

a circle

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 (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.

Diameter = 2 x radius of circle

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

Area of Circle:
area = PI r2 

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

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

Equation of Circle: (Cartesian coordinates)
graph circle
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(theta) = radius

for a circle with center with polar coordinates: (c, alpha) and radius a:
      r2 – 2cr cos(theta – alpha) + c2 = a2

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

parametric unit circle