IMO Shortlist 1995 problem G2
Dodao/la:
arhiva2. travnja 2012. Let
![A, B](/media/m/a/9/4/a94509f709e0a89fd467927301d3bf18.png)
and
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
be non-collinear points. Prove that there is a unique point
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
in the plane of
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
such that
%V0
Let $A, B$ and $C$ be non-collinear points. Prove that there is a unique point $X$ in the plane of $ABC$ such that $$XA^2 + XB^2 + AB^2 = XB^2 + XC^2 + BC^2 = XC^2 + XA^2 + CA^2.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1995