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!