Inside the convex polyhedron, the point $P$ and several lines $\ell_1,\ell_2, ..., \ell_n$ passing through $P$ and not lying in the same plane. To each face of the polyhedron we associate one of the lines $l_1, l_2, ..., l_n$ that forms the largest angle with the plane of this face (if there are there are several direct ones, we will choose any of them). Prove that there is a face that intersects with its corresponding line.