Školjka IMO Shortlist 1988 problem 18
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Consider 2 concentric circle radii 
and 
(
) with centre 
Fix 
on the small circle and consider the variable chord 
of the small circle. Points 
and 
lie on the large circle; 
are collinear and 
is perpendicular to 
i.) For which values of
is the sum 
extremal?
ii.) What are the possible positions of the midpoints
of 
and 
of 
as varies?
and () with centre Fix on the small circle and consider the variable chord of the small circle. Points and lie on the large circle; are collinear and is perpendicular to i.) For which values of
is the sum extremal? ii.) What are the possible positions of the midpoints
of and of as varies? Izvor: Međunarodna matematička olimpijada, shortlist 1988