Losing contact

The figure above shows a smooth track in a vertical plane, consisting of two circular arcs $$AB$$ and $$BC$$ of same radius $$r=2\text{ m}.$$ The common tangent to the arcs, $$BD,$$ is horizontal. A small block placed on the track at a height $$h$$ (in centimeters) above $$BD$$ leaves the track at exactly the same depth below. Find $$h.$$

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