Lines Around a Circle

Geometry Level 5

Points \(A, B, C\) are given on circle \( \Gamma\) such that \( AB=BC\). The tangents at \(A\) and at \(B\) intersect again at point \(D\). The line \(CD\) intersects \(\Gamma\) again at \(E\). The line \(AE\) intersects \(BD\) at \(F\). If \(AD = 120\), what is the length of \(FB\)?

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