IMO Shortlist 1967 problem 1


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2. travnja 2012.
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The parallelogram ABCD has AB=a,AD=1, \angle BAD=A, and the triangle ABD has all angles acute. Prove that circles radius 1 and center A,B,C,D cover the parallelogram if and only
a\le\cos A+\sqrt3\sin A.
Izvor: Međunarodna matematička olimpijada, shortlist 1967