Let ABC be a scalene triangle. Extend side BC at both ends such that BD = AB and CE = AC. In triangles ABD and ACE draw perpendiculars BF and CG, and let J be the intersection of BF and CG. Is AJ the bisector for angle BAC?
Hint Show that <BDJ ≡ <BAJ, <CAJ ≡ <CEJ, <BDJ ≡ <CEJ.