🚀 go-pugleaf

I posted this puzzle a long time ago on this newsgroup but 
did not get back any *correct* response. One response which
*appeared* correct at first glance had a serious flaw in it.
This problem has a history. You may skip the next paragraph
and cut right to the chase if you're impatient to go through
the history.

In high school, I was given this geometry problem (as a homework
assignment) which resisted every attempt at solving.  None of
the students, me including (can you believe it ?  :) :) :) :))
or the teacher could solve this problem either,
and in the end, the teacher conceded defeat and was somewhat
apologetic about giving us this innocent-looking killer that he
pulled off the top of his head. I am still mystified by the problem 
and wish to know if it has a simple, neat, geometrical solution (or
any other solution, though a geometrical one would be most welcome
as my high-school trigonometry has become too rusty).

Prove that if two angle bisectors of a triangle are of equal
length, (as measured from the vertex to the point of intersection
with the opposite side), the triangle is isosceles.

Kanad Chakraborty