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I'm really curious to know any relationships between the altitude of a tetrahedron and how the foot of this altitude splits the base triangle. For example if you have a tetrahedron PABC with apex P, and then you drop the altitude from P to the opposite base how does it split this base? Is the foot of the altitude the centroid/incenter/orthocenter of the base? Are there any special properties related to this?

Thanks :)

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    Are you talking about a regular tetrahedron with equilateral faces, or an arbitrary tetrahedron? If the latter, the foot of the altitude can be anywhere: just move the point $P$ around.2012-11-22
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    Hi, I was referring to any tetrahedron. Hmm that's true, but the reason I'm asking this question is that I'm trying to grasp what's so special about the tetrahedron in the following question and how does its altitude split the base triangle:2012-11-22
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    http://en.wikipedia.org/wiki/Schl%C3%A4fli_orthoscheme2012-11-22
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    Damn it, contest problem: http://www.mathcomp.leeds.ac.uk/2012-11-22
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    @user45220: Please do not post new questions as answers.2012-11-22
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    What's special about the tetrahedron in your now-deleted quote is that three of its faces are orthogonal.2012-11-22

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