Bullseye Illusion

Classic Problem

 * Bullseye-Illusion.png

The circle of radius $3 a$ at the center has the same area as the outer annulus whose width is $1$.

However, it appears to be larger.

Proof
From the diagram, it is seen that the circles are evenly spaced.

Let $C$ denote the circle of radius $3 a$ at the center, colored orange.

Let $A$ denote the outer annulus of width $a$ and outer radius $5 a$, colored blue.

We have that:

Hence the result.