IMO Shortlist 1969 problem 53
Dodao/la:
arhiva2. travnja 2012. ![(POL 2)](/media/m/2/9/1/2915ced399da23d63a8434d7a3ef63fd.png)
Given two segments
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
and
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
not in the same plane, find the locus of points
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
such that
%V0
$(POL 2)$ Given two segments $AB$ and $CD$ not in the same plane, find the locus of points $M$ such that $MA^2 +MB^2 = MC^2 +MD^2.$
Izvor: Međunarodna matematička olimpijada, shortlist 1969