1989 APMO Problems/Problem 3

Problem

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 $n = 1$ , $2$ , and $3$ , suppose that $B_n$ is the midpoint of $A_n A_{n+1}$ , and suppose that $C_n$ is the midpoint of $A_n B_n$ . Suppose that $A_n C_{n+1}$ and $B_n A_{n+2}$ meet at $D_n$ , and that $A_n B_{n+1}$ and $C_n A_{n+2}$ meet at $E_n$ . Calculate the ratio of the area of triangle $D_1 D_2 D_3$ to the area of triangle $E_1 E_2 E_3$ .

Page

Toolbox

Search

1989 APMO Problems/Problem 3

Problem

Solution