Question 12
(NET 4) IMO1. On the sides of a square $ABCD$ one constructs inwardly equilateral triangles $ABK,BCL,CDM,DAN$. Prove that the midpoints of the four segments $KL,LM,MN,NK$, together with the midpoints of the eight segments $AK,BK,BL,CL,CM,DM,DN,AN$, are the $12$ vertices of a regular dodecagon.