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Could somebody help me prove that the plane KLM, where K, L, M are feet of altitudes of an orthocentric tetrahedron ABCS inscribed in a sphere is parallel to the base ABC of this pyramid?

I would really appreciate it if you could help me with this problem.

Thank you in advance.

Mike

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If the tetrahedron is regular this is trivially by true by symmetry, if it isn't it isn't true in general. So, do you want to tell us more about your tetrahedron? – Phira Dec 3 '11 at 20:28
Well, this tetrahedron is orthocentric and inscribed in a sphere. – MickeyMouse Dec 4 '11 at 7:05
Ok, why do you tell us that it is inscribed in a sphere? This is true for every tetrahedron. You cannot expect people to spend time on your problem if the statement is probably faulty. State the question correctly and tell us context. If you saw the question in a book or a course, it is highly likely that you also saw useful properties of tetrahedra there. – Phira Dec 5 '11 at 15:20

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