(061) O2

Part of 1984 Tournament Of Towns

Problems(1)

TOT 061 1984 Spring S-O2 S-A2 6 altitudes in tetrahedron. // lines to a plane

Source:

Six altitudes are constructed from the three vertices of the base of a tetrahedron to the opposite sides of the three lateral faces. Prove that all three straight lines joining two base points of the altitudes in each lateral face are parallel to a certain plane.
(IF Sharygin, Moscow)

geometry3D geometrytetrahedronparallelPlanealtitude