Find the origin point of line

Hello all,

This problem is related to space research - So I am viewing two stars from a same viewpoint (36000kms away from Earth, for example- But I don't know the exact distance between viewpoint and Earth). The line of sights (line of sights are nothing but two lines from the viewpoint to the stars) to these two stars intersects the Earth Sphere at two points(these points form the tangent points, and lines are tangents) . I have only the Direction cosines of these two line of sights . I can assume the Earth Center as(0,0,0) and Earth Radius is also assumed. I am telling two lines, if one is sufficient then only one line can be considered, if more that two lines are required those observations also I will get-But I don't have any information abt tangent point locations or any other points on these lines, I have only Direction cosines of these lines. I want to get back the location of the viewpoint (x,y,z) . How can I do it ??? Thanks.I tried some methods . In all those at least one point of the line should be known to define the line,which I don't have.(Crying).