Question 54
Let $\triangle ABC$ be an equilateral triangle. Points $C_1$ and $C_2$ lie on side $AB$, points $B_1$ and $B_2$ lie on side $AC$, and points $A_1$ and $A_2$ lie on side $BC$, such that $\overline{A_1A_2} = \overline{B_1B_2} = \overline{C_1C_2}$. Let the lines $A_2B_1$ and $B_2C_1$, $B_2C_1$ and $C_2A_1$, $C_2A_1$ and $A_2B_1$ intersect at $E$, $F$, $G$ respectively. Prove that the triangle formed by the segments $B_1A_2$, $A_1C_2$ and $C_1B_2$ is similar to $\triangle EFG$.
