KöMaL 2008 C941

There are two lamps on the ceiling of a rectangular classroom of length 10 m. They emit conical light beam of apex angles of $90^o$. One is situated in the middle of the ceiling, and illuminates a circle of diameter 6 m on the floor. The lampshade of the other lamp is turned so that the illuminated region on the floor is long enough to draw a line segment of length 10 m on it in the direction parallel to the length of the room, but no light falls on the walls at the ends of the room. Find the distance between the two lamps.