IMO Shortlist 1967 problem 4


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2. travnja 2012.
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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