Let's say I have a triangle $ABC$, the middle of the sides are called A', B' and C'.
I have proved that $\Omega$, the orthocenter of $ABC$, is the barycentre of A'B'C' with masses $\tan \alpha$, $\tan \beta$ and $\tan \gamma$ on A', B' and C'. Now I have to deduce from this that $\Omega$ is also the barycentre of $A$, $B$ and $C$ with masses $a$, $b$ and $c$. I want to find $a, b, c$ so that $\Omega$ is the barycentre of $ABC$.
Thank you in advance!