It is known that if three numbers $x,y,z$ are the lengths of the edges of some triangle, then there exists a triangle with medians of length $x,y,z$. Also, if $x,y,z>0$ (no condition imposed) there exists a triangle with angle bisectors of length $x,y,z$ (the proof of this is very beautiful and uses Brouwer fixed point theorem).

I was wondering if there are some other results like this:

• if $x,y,z>0$ satisfy the family of conditions $ \{ C_1,C_2,...,C_n \}$(possibly void) then there exists a triangle for which the lengths of some important lines (for eg. symmedians) are $x,y,z$.

Do you know any such results?