We are given a convex four-sided pyramid with apex S and base face ABCD such that the pyramid has an inscribed sphere (i.e., it contains a sphere which is tangent to each race). By making cuts along the edges SA,SB,SC,SD and rotating the faces SAB,SBC,SCD,SDA outwards into the plane ABCD, we unfold the pyramid into the polygon AKBLCMDN as shown in the figure. Prove that K,L,M,N are concyclic. Tibor Bakos and Géza Kós geometry3D geometrypyramidsphereKvant