It is given a tetrahedron ABCD for which two points of opposite edges are mutually perpendicular. Prove that:(a) the four altitudes of ABCD intersects at a common point H;
(b) AH+BH+CH+DH<p+2R, where p is the sum of the lengths of all edges of ABCD and R is the radii of the sphere circumscribed around ABCD.H. Lesov geometry3D geometrytetrahedroninequalitiesgeometrical inequalities