2012 JBMO Problems
Let be positive real numbers such that . Prove that When does equality hold?
Let the circles and intersect at two points and , and let be a common tangent of and that touches and at and respectively. If and , evaluate the angle .
On a board there are nails, each two connected by a rope. Each rope is colored in one of given distinct colors. For each three distinct colors, there exist three nails connected with ropes of these three colors. a) Can be ? b) Can be ?
Find all positive integers and such that .
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