Mathematics for Carpenters and Builders - Carpenter's and Builder's Math, Plans, and Specifications - page 156

Figure 5-31 To describe an arc
of a circle with a given radius
through two given points.

C

A

B

Figure 5-32 To describe
an arc of a circle with a
given radius through two
given points, second
method.

A

D

G

O

B

E

F

C

In Figure 5-32, let A , B , and C be the given points, and proceed
as in Problem 10 to find the center O from which the circle may
be described. This problem is useful in such work as laying out an
object of large diameter (such as an arch) when the span and rise
are given.
Problem 12
To draw a tangent to a circle from a given point in the circumference.
In Figure 5-33, from A , lay off equal segments AB and AD . Join
line BD , and draw line AE parallel to BD for the tangent.
Problem 13
To draw tangents to a circle from points outside the circle.
In Figure 5-34, from A , and with the radius AC , describe an arc
BCD . From C , with a radius equal to the diameter of the circle,