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Volume of pyramid

Source: Dutch Mathematical Olympiad 1998

October 29, 2005
geometry3D geometrypyramid

Problem Statement

Let TABCDTABCD be a pyramid with top vertex TT, such that its base ABCDABCD is a square of side length 4. It is given that, among the triangles TABTAB, TBCTBC, TCDTCD and TDATDA, one can find an isosceles triangle and a right-angled triangle. Find all possible values for the volume of the pyramid.
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