In a tetrahedron ABCD the edges AD, BD, CD are equal. ABC Non-collinear points are chosen in the plane. A1, B1, C1 The lines DA1, DB1, DC1 intersect the surface of the sphere circumscribed about the tetrahedron at points A2, B2, C2, different from the point D. Prove that the points A1, B1, C1, A2, B2, C2 lie on the surface of a certain sphere. geometryspheretetrahedron3D geometry