Question 3
Let $A_1,A_2,A_3$ be three points in the plane, and for convenience let $A_4=A_1$, $A_5=A_2$. For $n=1,2,3$, let $B_n$ be the midpoint of $A_nA_{n+1}$ and $C_n$ the midpoint of $A_nB_n$. Suppose $A_nC_{n+1}$ and $B_nA_{n+2}$ meet at $D_n$, and $A_nB_{n+1}$ and $C_nA_{n+2}$ meet at $E_n$. Calculate the ratio of the area of triangle $D_1D_2D_3$ to that of triangle $E_1E_2E_3$.
Editorial clarification: assume the three initial points are noncollinear, so the requested area ratio is defined. The source omits this condition; its original wording is retained above.
Editorial clarification: assume the three initial points are noncollinear, so the requested area ratio is defined. The source omits this condition; its original wording is retained above.