For any piece wise smooth, simple closed curve $\gamma$ in the Euclidean plane $E^2$ and fix a point $G$ inside the area circled by $\gamma$.

**Show**: There exists three points $A,B$ and $C$ on the $\gamma$, such that $G$ become the barycenter of the triangle $\Delta ABC$ and $\Delta ABC$ locates inside the area circled by $\gamma$.

**Remark**:

It is not my idea, I just saw it on Weibo http://weibo.com/1648021814/EaRJiy1au?from=page_1005051648021814_profile&wvr=6&mod=weibotime&type=comment#_rnd1475372956164 , I think it is quite interesting , so I pose it.

Maybe there is theorem to admit it or a counter-example in computational geometry I do not know.