Hint: CE = 19
Well, you're given the perimeter=96 :
so "find" a triangle with integer sides and perimeter = 96 : very few!
With sides = a>b>c :
bisector from C = sqrt[ab(1 - k)] where k = c^2 / (a+b)^2
median from C = sqrt[2(a^2 + b^2) - c^2] / 2
And I gave median = 19 as clue...so not too difficult to wrap up.
I'll post/hide the solution (in case I forget!):
Spoiler: