2009 ToT Spring Senior A P4 3 planes cut parallelepiped into 8 hexahedrons
Source:
February 26, 2020
hexahedronparallelepiped3D geometrygeometrysphere
Problem Statement
Three planes dissect a parallelepiped into eight hexahedrons such that all of their faces are quadrilaterals (each plane intersects two corresponding pairs of opposite faces of the parallelepiped and does not intersect the remaining two faces). One of the hexahedrons has a circumscribed sphere. Prove that each of these hexahedrons has a circumscribed sphere.