The segment perpendicularly bisects at . Show that, subject to restrictions, there is a right circular cone whose axis passes through and on whose surface lie the points What are the restrictions?
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$(GBR 4)$ 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
Školjka 
The segment 
perpendicularly bisects 
at 
. Show that, subject to restrictions, there is a right circular cone whose axis passes through 
What are the restrictions?