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 r^{2}
if the angle is in radians, then area = ((/(2PI))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

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