  In one of the three 2010/2011 issues of the journal 'MathematicalSpectrum',
this author gave a three-parameter description of the entire set of integral
triangles(i.e. triangles with integer side lengths)and with a 120 degree
angle.This entire set expressed as a union of four families, see reference[5].
In this work we describe, in terms of three parameters again, the set of all
integral with a 120 degree angle, and whose bisectors of their 120 degree
angles; is also of integral length. To do so, we use the well known historic
theorem of Ptolemy for cyclic quadrilaterals, in conjunction with the general
positive integer solution of the equation, 1/z=1/x +1/y; and of course in
combination with the parametric description of the set of integral triangles
with a 120 degree angle mentioned above,The final results of this paper are
found in section8.
