Let (M, d) be a Euclidean metric space and  X and  Y distinct non-empty subsets of  M . Consider any elements  x ,  y and  z of  M , where  d(x,y) = d(x,z) + d(z,y) (i.e.,  z lies between  x and  y ). May the ratio of the Hausdorff distances between  z and  X and  z and  Y be then greater than the associated ratios for Hausdorff distances for  x and  y , i.e.:  \dfrac{d(z,X)}{d(z,Y)} > max \lbrace \dfrac{d(x,X)}{d(x,Y)}, \dfrac{d(y,X)}{d(y,Y)} \rbrace ?