What is the length of the marked segment?



The marked segment is the complement of a segment with length \(\dfrac{1}{2}\), see .
of a segment with length \(\dfrac{2\sqrt{3}-3}{3}\), see
, a segment with length \(\dfrac{2\sqrt{3}-3}{6}\) , see
and of a segment with length \(\dfrac{2-\sqrt{3}}{2}\), see .

Hence its length equals \[\dfrac{1}{2} - \dfrac{2\sqrt{3}-3}{3} - \dfrac{2\sqrt{3}-3}{6} - \dfrac{2-\sqrt{3}}{2} = \dfrac{2-\sqrt{3}}{2} \]