In $\Delta ABC$, $BE$ is the angle bisector of $\angle ABC$, $AD$ is the median on side $BC$. $AD$ intersects $BE$ at $O$ perpendicularly. If $AD = BE = 4$, find the lengths of each side of $\Delta ABC$.
What I Tried: At first I was having a hard time trying to make a bit of an accurate picture of the problem, and I made this :-
As solving this, I got no idea. Tried angle-chasing for example, if $\angle ABO = \angle DBO = x$ , then the green angles come to be $(90 - x)$ each, and then you have the brown angle to be $(90 + x)$ . You only get that $\Delta ABO \sim \Delta DBO$ , and that gives me no useful information for now.
I don't think I can use Pythagorean Theorem that much because except $AD = BE = 4$ , I have no other side-lengths to proceed. So right now, I am literally out of ideas.
Can anyone help me do this? Thank You!