Prove that pyramid ABCS is regular

In a pyramid with base $\displaystyle ABC$ and apex $\displaystyle S$ heights $\displaystyle AA'$,$\displaystyle BB'$,$\displaystyle CC'$,$\displaystyle SS'$ intersect at one point, situated inside the pyramid. Point $\displaystyle O$ is the center of a circumsphere of the pyramid. Prove that if line $\displaystyle SO$ is perpendicular to the plane $\displaystyle A'B'C'$, the pyramid $\displaystyle ABCS$ is regular.

A hint please at least... I have no good idea to solve this problem.