# Twisting the Problem - "Complicated Tangency of a system of circles"!

Geometry Level 4

Eight equal circles are mutually tangent in pairs and tangent externally to a unit circle as shown in the figure. If the common radius of the eight smaller circles can be expressed as:

$\large{\dfrac{\sqrt{A-\sqrt{B}}}{C - \sqrt{D-\sqrt{E}}}}$

for positive integers $$A, B, C, D, E$$ which doesn't have any square factor. Find the minimum value of $$A+B+C+D+E$$.

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