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An  arc  tangent  to  two  others  may  enclose both,  or  it  may  enclose  only  one  and  not the   other.   In   figure   4-38   the   problem   is to  draw  a  circular  arc  with  a  radius  equal to   AB,   tangent   to   and   enclosing   both   arcs CD    and    EF.    Set    a    compass    to    a    radius equal  to  AB  less  the  radius  of  CD  (indicated by  the  dashed  line  from  O),  and,  with  O as  a  center,   strike  an  arc.  Set  the  compass to   a   radius   equal   to   AB   less   the   radius of  EF  (indicated  by  the  dashed  line  from O´),  and,  with  O´  as  a  center,  strike  an  inter- secting  arc  at  P.  The  point  of  intersection  of these two arcs is the center of a circle of which an arc of given radius is tangent to, and encloses, both  arcs  CD  and  EF. In  figure  4-39  the  problem  is  to  draw a  circular  arc  with  a  radius  equal  to  AB, tangent  to,  and  enclosing,  CD,  and  tangent to,   but   NOT   enclosing,   EF.   Set   a   compass to   a   radius   equal   to   AB   less   the   radius of  arc  CD  (indicated  by  the  dashed  line  from 0),    and,    with    O    as    a    center,    strike    an arc,   Set   the   compass   to   AB   plus   the   radius of  EF  (as  indicated  by  the  dashed  line  from O´),  and,  with  O´  as  a  center,  strike  an  inter- secting arc at P. The point of intersection of the two arcs is the center of a circle of which an arc of the given radius is tangent to and encloses arc CD and also is tangent to, but does not enclose, arc EF. Figure 4-38.-Circular arc tangent to other circular arcs. and enclosing two Figure 4-39.-Circular arc tangent to and enclosing one arc and tangent to, but not enclosing, another. Figure 4-40.-Curve composed of a series of consecutive tangent circular arcs. COMPOUND  CURVES A  curve  that  is  made  up  of  a  series  of successive   tangent   circular   arcs   is   called   a compound  curve.  In  figure  4-40  the  problem  is to  construct  a  compound  curve  passing  through given  points  A,  B,  C,  D,  and  E.  First,  connect the  points  by  straight  lines.  The  straight  line between each pair of points constitutes the chord of  the  arc  through  the  points. Erect  a  perpendicular  bisector  from  AB.  Select an  appropriate  point  O1 on  the  bisector  as  a center, and draw the arc AB. From O1, draw the 4-13

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