The distance of a line segment from
the center to the points on the circle is
called the radius (or a line segment
whose endpoints are on any point on the
circle and its center). A line segment that
travels from one endpoint on the circle,
through the radius (center of the circle),
and to another endpoint directly oppo-
site is called the diameter;two times the
radius of a circle is the diameter. The
outer perimeter of the circle is called the
circumference. The chord of a circleis a
line segment whose two endpoints are on
the circle. Concentric circlesare two or
more circles that lie in the same plane
and have the same center, but with dif-
ferent radii. Circles with the same radius
are called congruent circles. (For more about circle measurements, see elsewhere in
this chapter.)Why are arcsand anglesimportant to circles?
Everything starts with the angle whose vertex is at the center of the circle (logically
called the central angle of a circle.) All the central angles of a circle add up to 360
degrees. Every central angle cuts the circle into two arcs:the minor arc(always less
than 180 degrees) and the major arc(always more than 180 degrees. Thus, the mea-
sure of the minor arc is actually the measurement of the central angle, while the mea-
surement of the major arc is 360 degrees minus the measure of the central angle. An
arc lengthis the distance between an arc’s endpoints along the path of the circle. Con-
gruent arcsare arcs with the same measurements. When the diameter of a circle sepa-
rates the circle into two congruent arcs it is called a semicircle.SOLID GEOMETRY
What is solid geometry?
Solid geometry is the study of objects in three-dimensional Euclidean space. It deals
with solids, as opposed to plane geometry, which deals with two dimensions. This part
of geometry is concerned with entities such as polyhedra, spheres, cones, cylinders, and
so on. (For more about Euclidean space and dimensions, see elsewhere in this chapter.)
In geometry, solids are defined as closed three-dimensional figures, or any limited
184 portion of space bounded by surfaces. They differ in subtle ways from what we perceive
The parts of a circle include the center (o), radius
(r), diameter (d), and circumference (c).