194 Section 2 Drafting Techniques and Skills
Figure 6-45. A—Constructing a line tangent to a given circle using a 45° triangle. B—A compass can also be
used for this construction.
Tangent
line
90–
P
P
A
B
C
Tangent
line
A B
Construct a Line
Tangent to a Circle
or Arc
Using a Triangle
A tangent is a line or curve that touches the t
surface of a circle or an arc at only one point. A
line drawn from the center of the circle or arc
to the point of tangency is perpendicular to
the tangent object. A tangent can be a straight
line. A tangent can also be a circle or an arc.
The following procedure is used to construct
a straight line tangent to a circle or arc.
1. Place a 45° triangle on a straightedge
so that the hypotenuse is against the
straightedge, Figure 6-45A. Adjust so
that one edge of the triangle is in line
with the center point of the circle and the
point of tangency (Point P).
2. Slide the triangle along the straightedge
until the other edge passes through
Point P. This will form the tangent line.
Using a Compass
1. With the point of tangency (Point P) as
the center point and the circle radius
PC, use a compass to construct an arc
through the center point of the circle
(Point C). This arc should pass through
Point C and a point on the circle, Point A,
Figure 6-45B.
2. With Point A as the center point and the
same radius PC, construct a semicircular
arc to pass through Point P. This semi-
circle should also extend to the opposite
side of Point A.
3. Extend Line CA until it intersects with
the semicircle at Point B.
4. Line BP is perpendicular to Line PC. This
line is also the required tangent line.