Curvilinear Polygons

Curvilinear Polygons

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The Arc drawing tool lets you make curvilinear polygons for which you can assign fill properties and find areas.  There are some limitations, however.  Since you can't construct point on two intersecting curves (except for circles), you have to connect curves with line segments.  If you want to connect two arcs, you have to first connect them with a line and move it to the intersection like this:

curvilinear parab 

To make a curvilinear polygon of the intersecting parabolas here are the steps:

  • Attach two lines.  
  • Make endpoints C and D -t point proportional along the curves.
  • Make endpoints A and B t point proportional along the curves.
  • Draw the two arcs - select Draw / Arc, from C to A and D to B.
  • Select the sides and arcs of the polygon in order and click Construct / Polygon.
  • Set t=2 in the Variables toolbox and the lines will become the intersection points.

curvilinear parab2 curvilinear parab3 

 

It's easier with circles because you can place points on their intersections:

intersecting circles1