Paraguayan National Olympiad 2010, Level 3, Problem 1
Source:
September 20, 2014
geometry
Problem Statement
The picture below shows the way Juan wants to divide a square field in three regions, so that all three of them share a well at vertex . If the side length of the field is meters, and each one of the three regions has the same area, how far must the points and be from ?Note: the area of each region includes the area the well occupies.[asy]
pair A=(0,0),B=(60,0),C=(60,-60),D=(0,-60),M=(0,-40),N=(20,-60);
pathpen=black;
D(MP("A",A,W)--MP("B",B,NE)--MP("C",C,SE)--MP("D",D,SW)--cycle);
D(B--MP("M",M,W));
D(B--MP("N",N,S));
D(CR(B,3));[/asy]