A regular n-gonal truncated pyramid is circumscribed around a sphere. Denote the areas of the base and the lateral surfaces of the pyramid by S1,S2, and S, respectively. Let σ be the area of the polygon whose vertices are the tangential points of the sphere and the lateral faces of the pyramid. Prove that
σS=4S1S2cos2nπ. geometry3D geometrypyramidspheretrigonometrycircumcircletrapezoid