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CIRCLE THROUGH THREE POINTS

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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. REGULAR  OCTAGON  AROUND A  GIVEN  INSCRIBED  CIRCLE Figure  4-30  shows  a  method  of  constructing a  regular  octagon  around  a  given  inscribed circle. Draw horizontal diameter AB and vertical diameter  CD.  Draw  tangents  at  A,  B,  C,  and  D perpendicular  to  the  diameters.  Draw  the remaining sides of the figure tangent to the circle at  45°  to  the  horizontal. CIRCULAR  CURVES Many   of   the   common   geometrical   con- structions occurring in the drafting room are those involving  circular  curves.  This  section  explains how  to  construct  circular  curves  that  may  be required  to  satisfy  varying  conditions. CIRCLE  THROUGH  THREE  POINTS In figure 4-31 the problem is to draw a circle (or a circular arc) that passes through points A, Figure 4-30.-Regular octagon around a circle. given inscribed Figure 4-31.-Circle or arc through three points. B, and C. Connect the points by lines and erect perpendicular  bisectors  as  shown.  The  point  of intersection of the perpendicular bisectors (O) is the center of the circle or arc passing through all three points. LINE  TANGENT  TO  A  CIRCLE AT  A  GIVEN  POINT A line that is tangent to a circle at a given point is perpendicular to the radius that intersects the 4-10



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