Dave's Math Tables: Circles

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 (): 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 = = 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 r²
    if the angle is in radians, then area = (/2)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() = radius

    for a circle with center with polar coordinates: (c, ) and radius a:
      r² - 2cr cos( - ) + 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