ISL 1989 Problem 65

Let $ABCD$ be a quadrilateral inscribed in a circle of radius $AB$ such that $BC = a, CD = b,$ $DA = \frac{3 \sqrt{3} - 1}{2} \cdot a$ For each point $M$ on the semicircle with radius $AB$ not containing $C$ and $D,$ denote by $h_1, h_2, h_3$ the distances from $M$ to the straight lines (sides) $BC, CD,$ and $DA.$ Find the maximum of $h_1 + h_2 + h_3.$