Figure 4-26.-Regular hexagon in a given circumscribed circle: one method.

Figure 4-27.-Regular hexagon in a given circumscribed circle: another method.

of constructing a regular hexagon in a given circumscribed circle. The diameter of the circumscribed circle has the same length as the long diameter of the hexagon. The radius of the circumscribed circle (which equals one-half the long diameter of the hexagon) is equal in length to the length of a side. Lay off the horizontal diameter AB and vertical diameter CD. OB is the radius of the circle. From C, draw a line CE equal to OB; then lay off this interval around the circle, and connect the points of inter-section. Figure 4-27 shows another method of constructing a regular hexagon in a given circumscribed circle. Draw vertical diameter AB, and use a T square and a 30/60 triangle to draw BC from B at 30 to the horizontal. Set a compass to BC, lay off this interval around the circumference, and connect the points of inter-section.

Figure 4-28 shows a method of constructing a regular hexagon on a given inscribed circle. Draw horizontal diameter AB and vertical center line. Draw lines tangent to the circle and perpendicular to AB at A and B. Use a T square and a 30/60 triangle to draw the remaining sides of the figure tangent to the circle and at 30 to the horizontal.

Figure 4-29.-Regular octagon in a given circumscribed circle.

REGULAR OCTAGON IN A CIRCUMSCRIBED CIRCLE GIVEN

Figure 4-29 shows a method of constructing a regular octagon in a given circumscribed circle. Draw horizontal diameter AB and vertical diameter CD. Use a T square and a 45 triangle to draw additional diameters EF and GH at 45 to the horizontal. Connect the points where the diameters intersect the circle.