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In certain math problem the only information about pyramid with quadrilateral base is that you can inscribe sphere inside. What kind of constraints was put on my pyramid ABCDS?

Is it something similar to situation where requirement to inscribe circle inside quadrilateral ABCD is that |AB| + |CD| = |BC| + |DA|?

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If you have a sphere touching all five faces, then its center has to lie on the bisecting planes of all dihedral angles. So all these planes have to meet in a single point. I assume that you'll want more explicit requirements, but perhaps this will give you a start. –  MvG Oct 21 '12 at 13:12
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