In the diagram, each of the three identical circles touch the other two.  The circumference of each circle is 36.  What is the perimeter of the shaded region? [asy]

defaultpen(1);

path p = (1, 0){down}..{-dir(30)}dir(-60){dir(30)}..{dir(-30)}((2, 0) + dir(-120)){-dir(-30)}..{up}(1, 0)--cycle;
fill(p, gray(0.75));

draw(unitcircle);
draw(shift(2 * dir(-60)) * unitcircle);
draw(shift(2) * unitcircle);
[/asy]
Question:
In the diagram, each of the three identical circles touch the other two.  The circumference of each circle is 36.  What is the perimeter of the shaded region? [asy]

defaultpen(1);

path p = (1, 0){down}..{-dir(30)}dir(-60){dir(30)}..{dir(-30)}((2, 0) + dir(-120)){-dir(-30)}..{up}(1, 0)--cycle;
fill(p, gray(0.75));

draw(unitcircle);
draw(shift(2 * dir(-60)) * unitcircle);
draw(shift(2) * unitcircle);
[/asy]
Answer:
Let's think step by step.

user
18
In the diagram, each of the three identical circles touch the other two.  The circumference of each circle is 36.  What is the perimeter of the shaded region? [asy]

defaultpen(1);

path p = (1, 0){down}..{-dir(30)}dir(-60){dir(30)}..{dir(-30)}((2, 0) + dir(-120)){-dir(-30)}..{up}(1, 0)--cycle;
fill(p, gray(0.75));

draw(unitcircle);
draw(shift(2 * dir(-60)) * unitcircle);
draw(shift(2) * unitcircle);
[/asy]
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