REGULAR PENTAGON ON AGIVEN INSCRIBED CIRCLETo construct a regular pentagon on a giveninscribed circle, determine the five equal intervalson the circle in the same manner. However,instead of connecting these points, draw each sideof the figure tangent to the circle at a point ofintersection.REGULAR HEXAGON IN AGIVEN CIRCUMSCRIBED CIRCLEMany bolt heads and nuts are hexagonal(six-sided) in shape. Figure 4-26 shows a methodFigure 4-26.-Regular hexagon in a given circumscribedcircle: one method.Figure 4-27.-Regular hexagon in a given circumscribedcircle: another method.of constructing a regular hexagon in a givencircumscribed circle. The diameter of thecircumscribed circle has the same length asthe long diameter of the hexagon. The radiusof the circumscribed circle (which equalsone-half the long diameter of the hexagon)is equal in length to the length of a side.Lay off the horizontal diameter AB andvertical diameter CD. OB is the radius ofthe circle. From C, draw a line CE equalto OB; then lay off this interval aroundthe circle, and connect the points of inter-section.Figure 4-27 shows another method ofconstructing a regular hexagon in a givencircumscribed circle. Draw vertical diameter AB,and use a T square and a 30°/60° triangle to drawBC from B at 30° to the horizontal. Set acompass to BC, lay off this interval around thecircumference, and connect the points of inter-section.REGULAR HEXAGON ON A GIVENINSCRIBED CIRCLEFigure 4-28 shows a method of constructinga regular hexagon on a given inscribed circle.Draw horizontal diameter AB and verticalcenter line. Draw lines tangent to the circle andperpendicular to AB at A and B. Use a T squareand a 30°/60° triangle to draw the remaining sidesof the figure tangent to the circle and at 30° tothe horizontal.Figure 4-28.-Regular hexagon on a given inscribed circle.4-9
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