This question somehow is unsolvable to me. Any idead/hints wil be much appreciated. 

![enter image description here](https://i.stack.imgur.com/fFmDg.jpg)

$AB$ is a chord which is cut ny the chords $CD$ and $EC$ in the circle.

Givens:
$\frown{AC} +\frown{BE}=\frown{AD}+\frown{BC}$

$S\_{CFG}=S\_{CGH}$

I need to show:

$AB \perp HG$

I realized that $CG$ is a median in $\triangle{HFG}$, so I'm trying to prove $CF=CG$ or $CG=GH$ which then will suffice to say that $\triangle{HFG}$ is a right triangle, but am not able to find a way.