## Prove that pyramid ABCS is regular

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

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