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AD/ sin \alpha=BD / sin \beta =CD/ sin \gamma in tetrahedron

Source: VIII All-Ukrainian Tournament of Young Mathematicians, Qualifying p3

May 25, 2021
3D geometrygeometrytetrahedronanglesUkrainian TYM

Problem Statement

Investigate the properties of the tetrahedron ABCDABCD for which there is equality ADsin⁡α=BDsin⁡β=CDsin⁡γ\frac{AD}{ \sin \alpha}=\frac{BD}{\sin \beta}=\frac{CD}{ \sin \gamma} where α,β,γ\alpha, \beta, \gamma are the values ​​of the dihedral angles at the edges AD,BDAD, BD and CDCD, respectively.
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