A CHORD is a line joining any two points lying on
a circle. (CD is a chord of circle O.)
An ARC is a portion of the closed curved lines
which forms the circle. It is designated by CD. An arc
is said to be subtended by a chord. Chord CD subtends
A TANGENT is a straight line which touches the
circle at one and only one point. (Line MZ is a tangent
to circle O.)
A CENTRAL ANGLE is an angle whose vertex is
the center of a circle and whose side are radii of the
circle. (As XOY, YOA, and XOB.)
CONCENTRIC CIRCLES are circles having the
same center and having different radii.
The CIRCUMFERENCE of a circle is the distance
around the circle. It is the distance on the curve from C
to A to X to Y to B to D and back to C.
Some examples of problems involving circles ap-
plicable to sheet metal work are as follows:
1. Construct a tangent to circle O by use of a
Step 1. Place the square in a position so that one
side touches the center and the other side
touches the circle.
A line drawn along the second side will be tangent to the
2. Divide a circle into 6 equal parts.
Step 1. Using a radius of the circle, begin at any
point, and step off chords equal to the
radius. If done accurately, this will make 6
divisions of the circle.
3. Divide a semicircle into 6 equal parts.
At O erect a perpendicular to AB.
With point A as the center and radius equal
to AO, swing an arc cutting the circle at E.
With point B as the center and the same
radius as in step 2, swing an arc cutting the
circle at F.
With the same radius, and point C as the
center, swing arcs cutting the circle at points
G and H,
AG = GE = EC = etc.
4. Divide a circle into 8 equal parts.
To divide circle O into 8 equal parts.
Draw diameter AB. Draw CD perpendicular
to AB, thus dividing the circle into 4 equal
Bisect the central angle COB. Mark the
point of the intersection of the bisector and