So you have a circle with radius 6. Now you have to attach clockwise equilateral triangles with side length 6 to it (from the outside) so that
a) The equilateral triangles do not overlap
b) Of every triangle one corner lies on the circle
c) Two triangles that are put down after each other share exactly one corner and this one lies not on the circle.
How many triangles can be attached to the circles without the triangles overlapping again?
Now prove that with that amount of triangles the first and last triangle share at least one corner.