Show that for any three points on the plane \(A,B\) and \(C\), \(AB \ge |BC - AC|\).
Prove the triangle inequality: in any triangle \(ABC\) the side \(AB < AC+ BC\).
In certain kingdom there are a lot of cities, it is known that all the distances between the cities are distinct. One morning one plane flew out of each city to the nearest city. Could it happen that in one city landed more than \(5\) planes?