ÖMO 1970 Problem 3

$E_1$ and $E_2$ are parallel planes and their distance is $p$ . (a) How long is the seitenkante of the regular octahedron such that a side lies in $E_1$ and another in $E_2$ ? (b) $E$ is a plane between $E_1$ and $E_2$ , parallel to $E_1$ and $E_2$ , so that its distances from $E_1$ and $E_2$ are in ratio $1:2$ Draw the intersection figure of $E$ and the octahedron for $P=4\sqrt{\frac32}$ cm and justifies, why the that figure must look in such a way