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.

http://www.mohawk.mtrsd.k12.ma.us/site/dept/math/jgalvagni/AMNB.bmp

Nice solution Bryan, this one had me stumped.  I made this using geometer's sketchpad and its really interesting to see the circles move as the triangle is manipulated.

I used color coded circles to transpose the segments from the triangle to the rays and back.  The solid circles are the preimages and the dashed circles are the images.  I used the same letters as Bryan, except B' is the image of B, etc...

If anyone wants the GSP file, I'd be happy to email it (or post it if I could figure out how)

Edited on April 28, 2005, 5:39 pm

Posted by Jer on 2005-04-28 17:38:03