Question 9
Initially we have a paper triangle $ABC$ such that $\angle BAC = 120^\circ$. In the first step, we draw the angle bisectors of the three angles of the triangle, which intersect in $I$, and then using a pair of scissors we cut along segments $AI$, $BI$ and $CI$, obtaining 3 triangles: $ABI$, $BCI$ and $CAI$. In the second step we repeat the same procedure with the three triangles, that is: each one of those is cut into three smaller triangles cutting along the angle bisectors. At the end of the second step we have 9 triangles in total. This procedure continues in the same way until we complete 10 steps.
How many of the triangles at the end of the process have an angle of $120^\circ$?
How many of the triangles at the end of the process have an angle of $120^\circ$?