Let A and B be different points on a circle with center O. With only a straightedge and a compass, can you construct a straight line through O meeting the segment AB at C, C strictly between A and B, and meeting the circle at D, so that C is between O and D and the segments AC and AD have the same length?
... it looks as if, when the condition is met, arc AD is half of arc BD, and therefore 1/3 of arc AB. If this is actually the case (I haven't proven), then accomplishing this would provide a way of trisecting angle BOA. But that's impossible with compass and straightedge.
Edited on July 20, 2005, 3:53 pm

Posted by Charlie
on 20050720 15:50:33 