Given a triangle ABC, how can you find a point P on AC and a point Q on BC, such that AP=PQ=QB?

N.B. A construction method is sought, and only compass and straightedge are allowed.

(In reply to re: Non-iterative solution by Bryan)

First of all, your solution is not a ruler-compass construction.  Moreover, your second paragraph claims, without proof, that there is a linear relation between the length of AM and the length of MN.  This claim is false!  As AM increases in length from zero, MN initially decreases from the length of AB.  However, eventually, M and N "pass over" C and the length of MN begins to increase as the length of AM increases.  Hence, without further argument, you can't claim that MN eventually equals the length of AM.

Posted by McWorter on 2005-05-04 04:09:14