501 Geometry Questions

Degrees and Arcs in Circle

Like polygons, circles contain degrees. A complete rotation around a cir-
cle contains 360°. A semicircleis half of a circle; it contains 180°. Any two
radii in a circle form a central anglethat will measure between 0° and 360°.
In the figure below ∠AOB is a central angle.
Two radii will also form an arc on the outside of the circle. Arcs formed
by central angles always have the same measurement as the central angle.
Arc AB in the circle pictured is written AB.
A minor arcis any arc that measures less than 180°. AB is a minor arc
measuring 33 ̊. A major arc is any arc that measures more than 180°. To
name a major arc, you must include an additional letter existing on the
perimeter of the circle, that is not a part of the minor arc. For example
ADB orACB are both ways to name the major arc measuring 327°.

A

B

C

D

O

33 ̊

327

diameter ̊

radiu

s

AOB = 33 ̊

AB = 33 ̊

AOB = AB

AB is a minor arc

ABC is a semicircle

ABD is a major arc

major arc

minor arc

A

B

C

D

O

diameter

OB and OD are each a radius

of O.

DB is a diameter

AC is a chord

OB > OD

2 × OB = DB

501 Geometry Questions