Head First 2D Geometry

4

10

circles

An arc is a section of the circumference

Covering part of the pizza crust with pepperoni creates an arc. That’s

geometry jargon for a section of the circumference of a circle—whether

it goes almost all the way around a circle, or just a tiny part of it.

Arcs can be described by the proportion of the circumference they

cover—a semicircle covers half—or by the angle of the corresponding

sector (the arc is the outside curved part of the sector).

I describe myself

as “four tenths

of a circle.”

I think of myself as

a 170 degree arc.

Sometimes arcs are described

as fractions. If you only

know the arc angle, then

you have to work out the

fraction.

144º

170º

144

360

=

o

Arc length is circumference x sector angle / 360

To find the length of an arc, first you need to find the circumference of

the circle the arc is part of. That means that you need either the diameter

or radius of the circle. Then you can use the sector angle to find out the

length of the part of the circumference that your arc covers.

Arc Length = 2

π

r × Sector Angle

360°

This calculation helps you find the

fraction of the circle that the

sector represents. If you already

know it’s 2/5 or 1/12, then just use

the fraction instead!

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