Question 26
The diagram shows a series of inscribed squares. The area of the largest outer square $ABCD$ is $512$. The first inner square is $A_1B_1C_1D_1$ where $AA_1=\frac14AB$, $BB_1=\frac14BC$, $CC_1=\frac14CD$ and $DD_1=\frac14DA$. The second inner square is $A_2B_2C_2D_2$ where $A_1A_2=\frac14A_1B_1$, $B_1B_2=\frac14B_1C_1$ and so on. The third inner square which is the smallest in the diagram is formed in a similar way. Find the area of the smallest square.
