Question 118
The incircle $\omega$ of equilateral triangle $ABC$ has radius $1$. Three smaller circles are inscribed tangent to $\omega$ and the sides of $ABC$, as shown. Three smaller circles are then inscribed tangent to the previous circles and to each of two sides of $ABC$. This process is repeated an infinite number of times. What is the total length of the circumferences of all the circles?
