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slightly longer than AB. Use a T square and a 45° triangle to draw AF and EB at 45° to AB and CD, Connect  AE  and  FB. SQUARE  IN  A  GIVEN CIRCUMSCRIBED CIRCLE Figure  4-20  shows  a  method  of  drawing  a square in a given circumscribed circle. Draw the diameters  AB  and  CD  at  right  angles  to  each other,  and  connect  the  points  where  the  diameters intersect  the  circumference  of  the  circle. SQUARE  CIRCUMSCRIBED  ON  A GIVEN INSCRIBED CIRCLE Figure 4-21 shows a method of circumscribing a  square  on  a  given  inscribed  circle,  Draw diameters  AB  and  CD  at  right  angles  to  each other. Then draw each side of the square tangent to  the  point  where  a  diameter  intersects  the circumference of the circle and perpendicular to the diameter. ANY  REGULAR  POLYGON  IN  A GIVEN  CIRCUMSCRIBED  CIRCLE You  can  construct  any  regular  polygon  in  a given circumscribed circle by trial and error with a drafting compass or dividers as shown in figure 4-22. To draw a nine-sided regular polygon in the circle  shown,  divide  the  circumference  by  trial  and error with a compass or dividers into nine equal segments, and connect the points of intersection. To  get  a  trial  spread  for  a  compass  or  dividers, divide the central angle subtended by the entire circle (360) by the number of sides of the polygon, in  this  case,  by  nine.  Then,  lay  off  the  central angle quotient from the center of the circle to the circumference  with  a  protractor. ANY  REGULAR  POLYGON  ON  A GIVEN  INSCRIBED  CIRCLE The same method (dividing the circumference into equal segments) can be used to construct a regular  polygon  on  a  given  inscribed  circle.  In  this case,  however,  instead  of  connecting  the  points of  intersection  on  the  circumference,  you  draw each  side  tangent  to  the  circumference  and Figure 4-20.-Square in a given circumscribed circle. Figure 4-21.-Square on a given inscribed circle. Figure 4-22.-Regular polygon in a given circumscribed circle. 4-7

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