APMO 1989 Q3: Geometry: Upper Secondary Mathematics Competition Question

Let A₁, A₂, A₃ be three points in the plane, and for convenience, let A₄ = A₁, A₅ = A₂. For n = 1, 2, and 3, suppose that B_n is the midpoint of A_nA_n+1, and suppose that C_n is the midpoint of A_nB_n. Suppose that A_nC_n+1 and B_nA_n+2 meet at D_n, and that A_nB_n+1 and C_nA_n+2 meet at E_n. Calculate the ratio of the area of triangle D₁D₂D₃ to the area of triangle E₁E₂E₃.

[APMO 1989 Q 3]

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