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 $a$ .

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Three Concentric Circles

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.