Normed planes in tangent cone to chord space of nonpositive curvature

We continue the cycle of papers devoted to study of the geometry of Busemann's $G$-spaces with distinguished family of segments (so-called chord spaces) which have non-positive curvature with respect to this family. We study the geometry of the tangent cone to chord space with non-positive curvature. It is shown that any two straight lines passing through the vertex of the cone span a weak normed plane, i. e., a weakly convex subset isometric to a plane with some norm.