In the pyramid of base $ABC$ and apex $S$, the heights $AA'$, $BB'$, $CC'$, $SS'$ cross in one point lying within the pyramid. Point $O$ is the center of the sphere circumscribed on this pyramid. Prove that if $SO$ is perpendicular to the plane $A'B'C'$, then the pyramid $ABCS$ is regular.
2026-03-30 09:48:27.1774864107
Proving the regularity of the pyramid
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