A Regular Tetrahedron in a Hemisphere

Problem

In the region

\{(x,y,z)\mid x^2+y^2+z^2\leqslant 1,\ z\geqslant 0\}

there exist four points whose pairwise distances all equal $d$ . Find the maximum value of $d$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, solid geometry, Casework

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