Outside of the plane of the triangle ABC is given point D.
(a) prove that if the segment DA is perpendicular to the plane ABC then orthogonal projection of the orthocenter of the triangle ABC on the plane BCD coincides with the orthocenter of the triangle BCD.
(b) for all tetrahedrons ABCD with base, the triangle ABC with smallest of the four heights that from the vertex D, find the locus of the foot of that height. geometry3D geometrytetrahedron