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.

I just made my solution public. This problem was posed to me when in High School, and I remember that my solution (the one given here) was way easier and shorter than the teacher's, which I think involved inversions of the plane or something like that.

Posted by Federico Kereki on 2005-05-10 19:49:55