2

Part of 1979 Polish MO Finals

Problems(1)

concurrency of lines joining vertices with incenters of opp. faces

Source: Polish MO Finals 1979 p2

Prove that the four lines, joining the vertices of a tetrahedron with the incenters of the opposite faces, have a common point if and only if the three products of the lengths of opposite sides are equal.

geometry3D geometrytetrahedron