Dave's Math Tables: Circles |

(Math | Geometry | 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.

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**