VietNam MO 1970-Pr.B2
Source:
February 18, 2007
geometry3D geometrytrigonometrygeometry proposed
Problem Statement
A plane passes through a vertex of a cube so that the three edges at the vertex make equal angles with . Find the cosine of this angle. Find the positions of the feet of the perpendiculars from the vertices of the cube onto . There are 28 lines through two vertices of the cube and 20 planes through three vertices of the cube. Find some relationship between these lines and planes and the plane .