In the interior of a square
we construct the equilateral triangles
Prove that the midpoints of the four segments
and the midpoints of the eight segments
are the 12 vertices of a regular dodecagon.
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In the interior of a square $ABCD$ we construct the equilateral triangles $ABK, BCL, CDM, DAN.$ Prove that the midpoints of the four segments $KL, LM, MN, NK$ and the midpoints of the eight segments $AK, BK, BL, CL, CM, DM, DN, AN$ are the 12 vertices of a regular dodecagon.
Školjka