Another prevalent kind of simple closed curve is a
circle. Circles are geometric figures whose
points all lie the same distance
from a given
point, the circle's center. They are not
polygons, because they are not made up of
segments. Points that lie in the
same line, like those in a
segment, are never
equidistant (an equal distance) from a single
point.

Circles are quite unlike any other geometric figure, so circles are governed by
a unique set of geometric rules. In the following lessons, these rules will be
laid out, but not expanded upon. We'll lay the foundation for studying the
angles within a circle, as well as those
outside a circle by defining certain characteristics of circles like arcs,
chords, diameters, radii, and central angles. Then we'll
discuss geometric figures that lie largely outside of a circle, like tangent
lines and secant lines. Finally the relationship between circles and
polygons will be explored.

The following lessons are an attempt to introduce some of the basic concepts
that concern circles--it is not a complete study of the relevance of circles
to geometry. These lessons will provide definitions and a few important
characteristics. In the Geometry 2 SparkNotes, we'll focus
more closely on solving for unknown parts and will explore in full the
characteristics of circles and their related geometric figures. Circles,
unlike polygons, actually do occur naturally in the world quite often. Most
situations that involve rotation involve circles and/or circular movement.
Rotation situations include reeling in a fishing line, driving in a vehicle with
wheels, and the spinning of the Earth. Even as you step out onto the street in
front of your house and turn around 360
degrees,
you become the center of a circle. A car parked fifty feet in front of you and
a tree standing fifty feet behind you are points on the same circle. Because
circles represent equidistance, they become a very prevalent shape in our world.
Here's a brief introduction to circles, their characteristics, and some of the
rules by which they are governed.