Three Concentric Circles

Geometry Level 4

Three concentric circles $A,B,C$ have the property that the radius of $A$ is bigger than the radius of $B$ , and the radius of $B$ is bigger than the radius of $C$ . A chord of circle $B$ of length $2$ is drawn such that it is tangent to circle $C$ ; a chord of circle $A$ of length $x$ is drawn such that it is tangent to circle $B$ . If the area between circle $A$ and $B$ is $2014$ times the area between circle $B$ and circle $C$ , then the value of $x$ can be expressed as $\sqrt{a}$ for some positive integer $a$ . Find the last three digits of $a$ .