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We solve the following geometric problem, which arises in several threedimensional applications in computational geometry: For which arrangements of two lines and two spheres in R 3 are there infinitely many lines simultaneously transversal to the two lines and tangent to the two spheres? We also treat a generalization of this problem to projective quadrics: Replacing the spheres in R 3 by quadrics in projective space P 3 , and fixing the lines and one general quadric, we give the followingdoi:10.1007/s00454-003-0789-4 fatcat:pdny6lgoz5djpetc3fdspgserq