[Ono's inequality](https://en.wikipedia.org/wiki/Ono%27s_inequality) is true for acute triangle but false with general triangles. The inequality as follows is false with general triangls but I think it true with acute triangle (follows answer by Fedor Petrov) 

The inequality as follows like the [Erdős–Mordell inequality](https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Mordell_inequality), I found a year ago, and sent the inequality to some people but I no have a proof until now.

>> Let $ABC$ be **acute triangle** (replaced general triangle by acute triangle following Fedor Petrov's answer)  with the centroid $G$, $D$ is the point in the plane. Let $EFH$ is a cevian triangle of $D$. How can prove that: 

>> $$DA+DB+DC \le 2(DE+DF+DH)+3DG$$

[![enter image description here][1]][1]



  [1]: https://i.sstatic.net/PdOqh.png