IMO Shortlist 1969 problem 27
Dodao/la:
arhiva2. travnja 2012. ![(GBR 4)](/media/m/9/c/7/9c7ede1698474e2e416d0da7cda17c1d.png)
The segment
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
perpendicularly bisects
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
at
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
. Show that, subject to restrictions, there is a right circular cone whose axis passes through
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
and on whose surface lie the points
![A,B,C,D.](/media/m/e/3/2/e32970d9069f0bebbf90b68ce6af289b.png)
What are the restrictions?
%V0
$(GBR 4)$ The segment $AB$ perpendicularly bisects $CD$ at $X$. Show that, subject to restrictions, there is a right circular cone whose axis passes through $X$ and on whose surface lie the points $A,B,C,D.$ What are the restrictions?
Izvor: Međunarodna matematička olimpijada, shortlist 1969