Rectangle with unit circles

Geometry Level 4

ABCD is a rectangle with AB=5. 2 circles of radius 1 are constructed inside the rectangle, one tangent to segments AB and AD, and the other tangent to BC and CD. Segment AC intersects the 2 circles at W, X, Y, Z in that order when going across the line. If WZ=23/Sqrt(5), then find BC.

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