Problem #PRU-78768

Problems Methods Pigeonhole principle Pigeonhole principle (angles and lengths) Geometry Plane geometry Polygons Sum of internal and external angles of polygons

Problem

It is known that a camera located at O cannot see the objects A and B, where the angle AOB is greater than 179. 1000 such cameras are placed in a Cartesian plane. All of the cameras simultaneously take a picture. Prove that there will be a picture taken in which no more than 998 cameras are visible.