point not on triangle plane, tetrahedron ABCD with heights drawn
Source: Bulgaria 1967 P4
June 23, 2021
geometry3D geometrytetrahedron
Problem Statement
Outside of the plane of the triangle is given point .
(a) prove that if the segment is perpendicular to the plane then orthogonal projection of the orthocenter of the triangle on the plane coincides with the orthocenter of the triangle .
(b) for all tetrahedrons with base, the triangle with smallest of the four heights that from the vertex , find the locus of the foot of that height.