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.