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 2012-03-09 12:06:36