Question 7
On the boundary of triangle $ABC$ points $D_1, D_2, E_1, E_2, F_1, F_2$ are chosen so that when going around the perimeter, the points are encountered in the following order: $A, F_1, F_2, B, D_1, D_2, C, E_1, E_2$. Given that $AD_1 = AD_2 = BE_1 = BE_2 = CF_1 = CF_2$, prove that two triangles formed by the triples of lines $AD_1, BE_1, CF_1$, and $AD_2, BE_2, CF_2$, have equal perimeters.