IMO 1985 LL TUR81

Given the side a and the corresponding altitude ha of a triangle

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IMO 1985 LL TUR81

Origin: TUR

Problem

Given the side a and the corresponding altitude ha of a triangle ABC, find a relation between a and ha such that it is possible to construct, with straightedge and compass, triangle ABC such that the altitudes of ABC form a right triangle admitting ha as hypotenuse.