IMO Shortlist 1967 problem 4
Dodao/la:
arhiva2. travnja 2012. Let
and
be two circles with centers
and
and equal radius
such that
. Let
and
be two points lying on the circle
and being symmetric to each other with respect to the line
. Let
be an arbitrary point on
. Prove that
%V0
Let $k_1$ and $k_2$ be two circles with centers $O_1$ and $O_2$ and equal radius $r$ such that $O_1O_2 = r$. Let $A$ and $B$ be two points lying on the circle $k_1$ and being symmetric to each other with respect to the line $O_1O_2$. Let $P$ be an arbitrary point on $k_2$. Prove that
$$PA^2 + PB^2 \geq 2r^2.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1967
Školjka 
