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5

Part of 1988 China National Olympiad

Problems(1)

China Mathematical Olympiad 1988 problem5

Source: China Mathematical Olympiad 1988 problem5

11/6/2013
Given three tetrahedrons AiBiCiDiA_iB_i C_i D_i (i=1,2,3i=1,2,3), planes αi,βi,γi\alpha _i,\beta _i,\gamma _i (i=1,2,3i=1,2,3) are drawn through Bi,Ci,DiB_i ,C_i ,D_i respectively, and they are perpendicular to edges AiBi,AiCi,AiDiA_i B_i, A_i C_i, A_i D_i (i=1,2,3i=1,2,3) respectively. Suppose that all nine planes αi,βi,γi\alpha _i,\beta _i,\gamma _i (i=1,2,3i=1,2,3) meet at a point EE, and points A1,A2,A3A_1,A_2,A_3 lie on line ll. Determine the intersection (shape and position) of the circumscribed spheres of the three tetrahedrons.
geometry3D geometrytetrahedronspheregeometry unsolved