CMO 1988 Problem 5

Given three tetrahedrons $A_iB_i C_i D_i$ ( $i=1,2,3$ ), planes $\alpha _i,\beta _i,\gamma _i$ ( $i=1,2,3$ ) are drawn through $B_i ,C_i ,D_i$ respectively, and they are perpendicular to edges $A_i B_i, A_i C_i, A_i D_i$ ( $i=1,2,3$ ) respectively. Suppose that all nine planes $\alpha _i,\beta _i,\gamma _i$ ( $i=1,2,3$ ) meet at a point $E$ , and points $A_1,A_2,A_3$ lie on line $l$ . Determine the intersection (shape and position) of the circumscribed spheres of the three tetrahedrons.