Question 3
Let $ABCD$ be a tetrahedron with $BA\perp AC$ and $DB\perp(BAC)$. Let $O$ be the midpoint of $AB$, and drop $OK\perp DC$. Prove that a necessary and sufficient condition for
$$\frac{V_{KOAC}}{V_{KOBD}}=\frac{AC}{BD}$$
is $2AC\cdot BD=AB^2$.
$$\frac{V_{KOAC}}{V_{KOBD}}=\frac{AC}{BD}$$
is $2AC\cdot BD=AB^2$.