Let OABCDEF be a hexagonal pyramid with base ABCDEF circumscribed around a sphere ω. The plane passing through the touching points of ω with faces OFA, OAB and ABCDEF meets OA at point A1, points B1, C1, D1, E1 and F1 are defined similarly. Let ℓ, m and n be the lines A1D1, B1E1 and C1F1 respectively. It is known that ℓ and m are coplanar, also m and n are coplanar. Prove that ℓ and n are coplanar. geometry3D geometrypyramidsphere