# Reflect on this...

Geometry Level 5

A square $$ABCD$$ of side length $$k$$ contains unit circles at each of corners $$B$$ and $$D$$ such that each circle is tangent to the square at precisely two points. A ray of light emanating from point $$A$$ reflects off each circle and then returns to $$A$$, creating a path in the shape of an equilateral triangle.

There is a unique value of $$k$$ for which this scenario can occur. Find $$\lfloor 10000\cdot k \rfloor$$.

Note: "Reflecting" means that the angle of incidence equals the angle of reflection.

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