Školjka

%V0 Three faces of a tetrahedron are right triangles, while the fourth is not an obtuse triangle. (a) Prove that a necessary and sufficient condition for the fourth face to be a right triangle is that at some vertex exactly two angles are right. (b) Prove that if all the faces are right triangles, then the volume of the tetrahedron equals one -sixth the product of the three smallest edges not belonging to the same face.