Tetrahedron inscribed in a sphere

Geometry Level pending

A tetrahedron ABCD is inscribed in a sphere of radius 12 cm and center O. Straight lines AO, BO, CO, DO intersect opposite faces(of the tetrahedron) at A' , B' , C'and D' respectively . Find the minimum possible value of sum of length of AA', BB', CC' and DD' (in cm)

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