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This article analyses a tightly packed random two-phase system possessing spherical particles having the volume fraction of 1/8. For a three-dimensional hard-core `dead leaves' model of spheres of constant diameter, the chord length distribution density of typical chords mi of the connected phase (outside the hard particles) is investigated. The calculation starts from the second derivative of the small-angle scattering correlation function of the model and applies characteristic functions. The result fulfills Rosiwal's linear integration principle.