Solved: Ellipsoid inside a tetrahedron (1946 Putnam Exam)
Chapter 12, Problem 76(choose chapter or problem)
Ellipsoid inside a tetrahedron (1946 Putnam Exam) Let P be a plane tangent to the ellipsoid x2>a2 + y2>b2 + z2>c2 = 1 at a point in the first octant. Let T be the tetrahedron in the first octant bounded by P and the coordinate planes x = 0, y = 0, and z = 0. Find the minimum volume of T. (The volume of a tetrahedron is one-third the area of the base times the height.)
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