OME 1974 Problem 6

Two chords are drawn in a circle of radius equal to unit, $AB$ and $AC$ of equal length. a) Describe how you can construct a third chord $DE$ that is divided into three equal parts by the intersections with $AB$ and $AC$ . b) If $AB = AC =\sqrt2$ , what are the lengths of the two segments that the chord $DE$ determines in $AB$ ?