We cannot trisect with three circles and one additional line

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

wpe4D.jpg (9163 bytes)wpe4E.jpg (15981 bytes)

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

wpe2.jpg (12221 bytes) wpe3.jpg (19997 bytes) wpe4.jpg (29450 bytes)

wpe5.jpg (17978 bytes) wpe6.jpg (12499 bytes) wpe7.jpg (18134 bytes)

wpe3F.jpg (15956 bytes) wpe40.jpg (24145 bytes) wpe45.jpg (45517 bytes)

wpe42.jpg (45576 bytes)  wpe44.jpg (23784 bytes)  wpe41.jpg (34205 bytes)

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

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