Extensions of a triangle

Geometry Level 4

Let be \(ABC\) an equilateral triangle of side \(1\). \(D\) and \(E\) points on the extension of \(AB\) and \(AC\), respectively such that\(AD=CE=1\) . \(F\) is the point of interseccion between \(DE\) and \(BC\) extension.

Find the length \(CF\) to 3 decimal places.

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