Joshua, Are you interested in knowing how to do this construction with a compass and a straightedge? If so, I can send you a solution, but I do not want to post one for others to see who might not want to see an answer.
On Fri, 7 Nov 1997, Joshua Zucker wrote:
> This is an interesting question! > Of course you can always solve it by analytic geometry, and then see > that all the quantities there are constructible, and construct them. > But that's pretty ugly! And I don't yet see any better way to do it. > > I have another construction problem which is similarly irritating to > me (where I can prove with analytic geometry that it's constructible, > but I can't find a nice construction, though the person who gave me > the problem implied there ought to be a nice one): > > Given triangle ABC, find points X and Y on AB and AC such that > BX = XY = YC. > > --Joshua Zucker >