RIOPLATENSE 1999 Problem 5

The quadrilateral $ABCD$ is inscribed in a circle of radius $1$ , so that $AB$ is a diameter of the circumference and $CD = 1$ . A variable point $X$ moves along the semicircle determined by $AB$ that does not contain $C$ or $D$ . Determine the position of $X$ for which the sum of the distances from $X$ to lines $BC, CD$ and $DA$ is maximum.