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 re: Initital exploration by Bractals)

You know what?   I never use the locus command.
(It may even be that I've never used it!)
I just created point D, a circle centered at C containing D and the other intersection (D').  Then I translated this circle to B and created two more intersections(E and E').  Then I drew both possible sets of BD and CE, traced their intersections (F and F'), and animated D.

Once this trace looked like a line I just connected F and F'.

I tried an algebraic solution earlier this afternoon but the terms went all 4th power on me.

Posted by Jer on 2012-03-10 00:34:58