IMO 1985 LL USA86

Let l denote the length of the smallest diagonal of all rectangles

imolonglistmathematicsolympiad

IMO 1985 LL USA86

Origin: USA

Problem

Let l denote the length of the smallest diagonal of all rectangles inscribed in a triangle T . (By inscribed, we mean that all four vertices of the rectangle lie on the boundary of T .) Determine the maximum value of l2 S(T ) taken over all triangles (S(T ) denotes the area of triangle T ).