This note introduces a geometric diagnostic framework for analyzing constrained two-channel systems using the Thales semicircle construction. Any partition of a conserved total between two non-negative quantities is mapped to a right triangle whose hypotenuse represents total capacity, whose altitude represents mutual coupling amplitude, and whose deviation from maximal altitude quantifies partition asymmetry (deficit). Three structural insights follow. First, what functions as “resistance” to mutual interaction in such systems is configurational rather than material: it arises from partition asymmetry and is independent of scale or intrinsic properties. Second, effective coupling is governed by the geometric mean of channel amplitudes, not by their arithmetic sum; equal partition maximizes joint participation, while asymmetry suppresses coupling. Third, inefficiency in coupled response corresponds to coupling capacity that is geometrically inaccessible, not to dissipation or loss. These observations are purely classificatory. The framework does not introduce new dynamics, derive constants, or modify existing physical theories. Instead, it provides a portable geometric language for describing constraint structure across domains. The gravitational two-body problem is used as an illustrative example, where the reduced mass emerges naturally as the geometric mean squared per unit capacity. The Thales construction thus offers a unified vocabulary for analyzing resistance, coupling, and inefficiency as properties of configuration space rather than of dynamics.