2000 JBMO Problems
Let and be positive reals such that Show that .
Find all positive integers such that is the square of an integer.
A half-circle of diameter is placed on the side of a triangle and it is tangent to the sides and in the points and respectively. Prove that the intersection point between the lines and lies on the altitude from of the triangle .
At a tennis tournament there were boys and girls participating. Every player played every other player. The boys won times as many matches as the girls. It is knowns that there were no draws. Find .
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