Problems from IMO 1960

1-Find all the three-digit numbers for which one obtains, when dividing the number by 11, the sum of the squares of the digits of the initial number.

2-For which real numbers x does the following inequality hold :

3-A right-angled triangle ABC is given for which the hypotenuse BC has length a and is divided into n equal segments, where n is odd. Let α be the angle with which the point A sees the segment containing themiddle of the hypotenuse.Prove that:

where h is the height of the triangle.


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