A sphere S lies within tetrahedron ABCD, touching faces ABD,ACD, and BCD, but having no point in common with plane ABC. Let E be the point in the interior of the tetrahedron for which S touches planes ABE, ACE, and BCE as well. Suppose the line DE meets face ABC at F, and let L be the point of S nearest to plane ABC. Show that segment FL passes through the centre of the inscribed sphere of tetrahedron ABCE.KöMaL A.723. (April 2018), G. Kós 3D geometrygeometryspheretetrahedroncollinear