Figure 4-23.-Regular polygon on a given inscribed circle.perpendicular to the radius at each point ofintersection, as shown in figure 4-23.ANY REGULAR POLYGON WITH AGIVEN LENGTH OF SIDEFigure 4-24 shows a method of drawing anyregular polygon with a given length of side. Todraw a nine-sided regular polygon with length ofside equal to AB, first extend AB to C, makingCA equal to AB. With A as a center and AB (orFigure 4-24.-Any regular polygon with a given length ofside.CA) as a radius, draw a semicircle as shown.Divide the semicircle into nine equal segmentsfrom C to B, and draw radii from A to the pointsof intersection. The radius A2 is always thesecond side of the polygon.Draw a circle through points A, B, and D.To do this, first erect perpendicular bisectorsfrom DA and AB. The point of intersection ofthe bisectors is the center of the circle. Thecircle is the circumscribed circle of the polygon.To draw the remaining sides, extend the radiifrom the semicircle as shown, and connect thepoints where they intersect the circumscribedcircle.Besides the methods described for constructingany regular polygon, there are particular methodsfor constructing a regular pentagon, hexagon, oroctagon.REGULAR PENTAGON IN AGIVEN CIRCUMSCRIBED CIRCLEFigure 4-25 shows a method of constructinga regular pentagon in a given circumscribedcircle. Draw a horizontal diameter AB and avertical diameter CD. Locate E, the midpoint ofthe radius OB. Set a compass to the spreadbetween E and C, and, with E as a center, strikethe arc CF. Set a compass to the spread betweenC and F, and, with C as a center, strike the arcGF. A line from G to C forms one side of thepentagon. Set a compass to GC and lay off thisinterval from C around the circle. Connect thepoints of intersection.Figure 4-25.-Regular pentagon in a given circumscribedcircle.4-8
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