Let $\triangle ABC$ be an acute triangle. $X$ is a point inside $\triangle ABC$ such that \[AX^2+MX^2=BX^2+NX^2=CX^2+PX^2\] where $M$, $N$, $P$ are the projection of $X$ is $BC$, $AC$, $AB$ respectively. Find the value of $\frac{HX}{OH}$ where $O$ and $H$ are the circumcenter and incenter of $\triangle ABC$ respectively.