MathDB
orthocentric tetrahedron, strict inequality

Source: Bulgaria 1972 P6

June 21, 2021
geometry3D geometrytetrahedroninequalitiesgeometrical inequalities

Problem Statement

It is given a tetrahedron ABCDABCD for which two points of opposite edges are mutually perpendicular. Prove that:
(a) the four altitudes of ABCDABCD intersects at a common point HH; (b) AH+BH+CH+DH<p+2RAH+BH+CH+DH<p+2R, where pp is the sum of the lengths of all edges of ABCDABCD and RR is the radii of the sphere circumscribed around ABCDABCD.
H. Lesov