We cannot trisect with three circles and one additional line

We first consider the two different ways we can construct two circles. 

We now show the thirteen possible different ways to add a third circle.   

None of these trisect the segment, so three circles alone is not enough.  Nor would adding any line through two of their intersection points produce a trisection, so three circles and one additional line is not enough. 

Return to Four Circles Trisection Page

         Villanova Home Page         Math Dept Home Page  8 Feb 2001