Let ABC be a triangle with points D and E lying on lines AC and AB respectively such that D and E are on the same side of line BC and |BE| = |CD| > 0. Let F be the intersection of rays BD and CE.

What is the locus of the intersections F?

Prove it.

(In reply to Initital exploration by Jer)

I've found a problem with Sketchpad when
constructing loci. With respect to this
problem, let point D on line CA be the
independent variable. To locate point E
on line AB I construct a circle with B
as the center and radius |CD|. This circle
intersects line AB at two points. In real
time it's easy to pick which to label E,
but when running the locus Sketchpad has
no way to determine which point to pick.
Therefore, I end up creating the locus
in two steps: 1) pick point D on the same
side of line BC as vertex A and 2) pick
point D on the other side. Have you run 
into this problem when creating loci?

Posted by Bractals on 2012-03-09 15:09:04