Chapter 15: Circles 199Arcs are named by the points at each end of the arc, with an arc symbol over the top, but that
isn’t always enough information. The notation AC means the minor arc that is the shorter path
along the circle from A to C, but you might want to name the major arc that goes around the
circle in the other direction from A to C. To show that you want a major arc, include another
letter of a point on the major arc to show which way you want to travel. So ABC names the major
arc from A through B to C.
Most of the units of measurement you use were designed for lines, so when you get to circles,
you need a different way of measuring. The type of measuring you want to do in circles is much
more like measuring an angle than measuring a line, so you borrow the system of degrees for use
in circles. Degrees measure the rotation, how far you turn around a point. A circle turns all the
way around its center point until it meets itself again. That full rotation is 360r. There are 360r
in a full circle and 180r in a semicircle. Every arc can be assigned a measurement as a number of
degrees, according to what part of the circle it is. Minor arcs are less than 180r and major arcs
are more than 180r. A quarter of the circle is one-fourth of 360r, or 90r.
One circle, all by itself, is pretty, but there’s not a lot to say about it. Its center controls where it
is, its radius controls how big it is, and it’s always the same shape. If you have two or more circles,
they can begin to interact a little bit. You can have two circles that just barely touch each other
and have just one point in common. Those are tangent circles.
Tangent circles touch at only one point.One circle can be tangent to another from outside or from inside.
If the circles are externally tangent, they can be the same size
or different sizes, but to be internally tangent, they’ll have to be
different sizes or they’ll just sit right on top of one another. If a
smaller circle is placed inside a larger one so that their centers are
aligned, they won’t touch each other, but they are concentric circles,
circles with the same center.
Concentric circles are circles
with the same center.