A Sphere Around a Tetrahedron

★ 6/10solid geometryCirclesSymmetry

Problem

The four vertices of tetrahedron P-ABCP\text{-}ABC lie on a sphere OO. We have PA=PB=PCPA = PB = PC, triangle ABCABC is equilateral with side length 22, and E,FE, F are the midpoints of ACAC and BCBC respectively, with ∠EPF=60∘\angle EPF = 60^\circ. Find the surface area of sphere OO.

Answer

Solution

Difficulty6/10
Topicssolid geometry, Circles, Symmetry

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