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2019 G4: Cube in a Right Tetrahedron

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January 27, 2019
geometry3D geometrytetrahedron

Problem Statement

Suppose T=A0A1A2A3\mathcal{T}=A_0A_1A_2A_3 is a tetrahedron with ∠A1A0A3=∠A2A0A1=∠A3A0A2=90∘\angle A_1A_0A_3 = \angle A_2A_0A_1 = \angle A_3A_0A_2 = 90^\circ, A0A1=5,A0A2=12A_0A_1=5, A_0A_2=12 and A0A3=9A_0A_3=9. A cube A0B0C0D0E0F0G0H0A_0B_0C_0D_0E_0F_0G_0H_0 with side length ss is inscribed inside T\mathcal{T} with B0∈A0A1‾,D0∈A0A2‾,E0∈A0A3‾B_0\in \overline{A_0A_1}, D_0 \in \overline{A_0A_2}, E_0 \in \overline{A_0A_3}, and G0∈△A1A2A3G_0\in \triangle A_1A_2A_3; what is ss?
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