sould policemen know geometry? a criminal problem
Source: Sharygin Geometry Olympiad 2016 Final Round problem 8 grade 8
July 22, 2018
geometryproblem
Problem Statement
A criminal is at point , and three policemen at points and block him up, i.e. the point lies inside the triangle . Each evening one of the policemen is replaced in the following way: a new policeman takes the position equidistant from three former policemen, after this one of the former policemen goes away so that three remaining policemen block up the criminal too. May the policemen after some time occupy again the points and (it is known that at any moment does not lie on a side of the triangle)?by V.Protasov