Investigate the properties of the tetrahedron $ABCD$ for which there is equality $$\frac{AD}{ \sin \alpha}=\frac{BD}{\sin \beta}=\frac{CD}{ \sin \gamma}$$where $\alpha, \beta, \gamma$ are the values of the dihedral angles at the edges $AD, BD$ and $CD$, respectively.
Problem
Source: VIII All-Ukrainian Tournament of Young Mathematicians, Qualifying p3
Tags: 3D geometry, geometry, tetrahedron, angles, Ukrainian TYM