Date: Nov 7, 1997 4:16 PM
Author: Joshua Zucker
Subject: construction of triangle of given perimeter, given point and angle
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.