be an acute, scalene triangle, and let 
,
,
be the midpoints of 
,
,
,
intersect ray 
in points 
and 
respectively, and let lines 
and 
intersect in point 
,
,
Y by
Given six distinct points on a plane, all pairwise distances between which are different. Prove that there exists a line segment connecting two of these points which is the longest side in one triangle formed by three of the points, and the shortest side in another triangle formed by three of the points.
