A plane mirror of circular shape with radius r=20 cm is fixed to the ceiling. A bulb is to be placed on the axis of the mirror. A circular area of radius R=1 m on the floor is to be illuminated after reflection of light from the mirror. The height of the room is 3 m. The maximum distance from the centre of the mirror and the bulb so that the required area is illuminated is 15x (cm). Find x.