IMO 1985 LL VIE97

Origin: VIE

Problem

In a plane a circle with radius R and center w and a line \Lambda are given. The distance between w and \Lambda is d, d > R. The points M and N are chosen on \Lambda in such a way that the circle with diameter MN is externally tangent to the given circle. Show that there exists a point A in the plane such that all the segments MN are seen in a constant angle from A.