A sphere
is tangent to the edges
of a tetrahedron
at the points
respectively. The points
are the vertices of a square. Prove that if the sphere is tangent to the edge
, then it is also tangent to the edge
%V0
A sphere $S$ is tangent to the edges $AB,BC,CD,DA$ of a tetrahedron $ABCD$ at the points $E,F,G,H$ respectively. The points $E,F,G,H$ are the vertices of a square. Prove that if the sphere is tangent to the edge $AC$, then it is also tangent to the edge $BD.$
Školjka