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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