Problem

Source: I Caucasus 2015 11.4

Tags: geometry, 3D geometry, pyramid, 3-Dimensional Geometry



The midpoint of the edge $SA$ of the triangular pyramid of $SABC$ has equal distances from all the vertices of the pyramid. Let $SH$ be the height of the pyramid. Prove that $BA^2 + BH^2 = C A^2 + CH^2$.