Ordered Points on a Line

Geometry Level 4

Let \(A, B, C, D, E\) and \(F\) be points on a line in that order such that \(AB=BC=CD=DE=EF = 15\). Let \( \Gamma_1\) be the circle with center \(D\) and radius \(CD\), and let \(\Gamma_2\) be the circle with center \(F\) and radius \(EF\). Let \(l\) be the tangential line from \(A\) to \(\Gamma_2\). \(l\) intersects \(\Gamma_1\) at points \(X\) and \(Y\). What is the length of \(XY\)?

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