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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