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.
By drawing this on geometer's sketchpad the locus appears to be a line. I'll assume it is.
This line does not appear to have much to do with the triangle except that it passes through BC. Also if angle B < angle C the line passes through side AB and if angle C < angle B the line passes through side AC and if the angles are equal the line passes through A.

Posted by Jer
on 20120309 12:06:36 