Question 5
In the tetrahedron $ABCD$, the edges $BD$ and $CD$ are mutually perpendicular, and the projection of the vertex $D$ to the plane $ABC$ is the intersection of the altitudes of the triangle $ABC$. Prove that
$$(AB+BC+CA)^2\le6(DA^2+DB^2+DC^2).$$
For which tetrahedra does equality hold?
$$(AB+BC+CA)^2\le6(DA^2+DB^2+DC^2).$$
For which tetrahedra does equality hold?