b.

In many problems involved in tool work, exact measurements can be

obtained only by the use of accurately ground plugs. The solution of such

problems involves several principles of layout work which must be thoroughly

understood. A plug inserted in an opening can be represented by a circle

touching two surfaces, as shown in figure 25.

FIGURE 25.

LAYOUT OF PLUG INSERTED IN OPENING.

The points of contact, A and B are called the "points of tangency".

A

tangent to a circle is perpendicular to the radius at the point of tangency;

thus, DC makes a right angle with radius AO. Two tangents drawn from the

same point to a circle are equal; hence, DA = DB.

A line, joining the

center of a circle with the intersection of two tangents, bisects the angle

between the tangents; thus, line OD bisects angle ADB.

EXAMPLE

Find the dimension of X in figure 26, view A, on the following page.