CMO 1982 Problem 1

In the diagram, $OB_i$ is parallel and equal in length to $A_i A_{i + 1}$ for $i = 1$ , 2, 3, and 4 ( $A_5 = A_1$ ). Show that the area of $B_1 B_2 B_3 B_4$ is twice that of $A_1 A_2 A_3 A_4$ .