Question 1012098
Better expression, the bisector for that angle is  {{{4sqrt(3)}}}.


Use Triangle Angle Bisector Theorem, and Law of Cosines.


Draw the triangle, 6, 9, angle bisector between them being 4sqrt(3), the x side being adjascent to the 6, the y side adjascent to the 9.  Let {{{2*alpha}}} be the angle measure between the 6 and the 9.


{{{system(6/9=2/3=x/y,6^2+(4sqrt(3))^2-2*6*4sqrt(3)cos(alpha)=x^2,(4sqrt(3))^2+9^2-2*4sqrt(3)cos(alpha)=y^2)}}}


This is only a start, far from finished.