The trial-and-error method also can be used in

drawing a circle through three given points. In figure

14-16, view A, arcs with an equal radius have been

The following steps tell you how to draw a reverse

drawn from each of the three points. You can see that

or ogee curve. Refer to figure 14-17 as you read this

they fail to have a common point of intersection and are,

section.

therefore, not at the proper center.

1. Erect a perpendicular at point A and drop one at

If the arcs from the two outer points intersect below

point B (view A).

the center point arc (view B), you know that the radius

of the circle is larger. If the two outer points intersect

2. Connect points A and B with a line (view B).

above the center point arc, then the radius of the circle

3. Assume a point (C) on this line through which

is smaller.

the curve will pass. This point may be the

From this trial you can judge where the center will

midpoint of the line if equal arcs are desired.

probably fall. Select a point (O) to use as the center in

4. Bisect AC and CB, as shown in view C. The

drawing your first trial arc. If this trial arc fails to pass

i n t e r s e c t i o n of these lines with the

through the three points perfectly (view B), move the

perpendiculars from points A and B are the

center, as shown in view C.

centers of the required arcs. Complete the

This time you can judge the position of the center

curve, as shown in view D.

so accurately that the circle may be drawn through the

points (view C).

14-12