[en] It is known that relative entropy of entanglement for an entangled state ρ is defined via its closest separable (or positive partial transpose) state σ. Recently, it has been shown how to find ρ provided that σ is given in a two-qubit system. In this article we study the reverse process, that is, how to find σ provided that ρ is given. It is shown that if ρ is of a Bell-diagonal, generalized Vedral-Plenio, or generalized Horodecki state, one can find σ from a geometrical point of view. This is possible due to the following two facts: (i) the Bloch vectors of ρ and σ are identical to each other; (ii) the correlation vector of σ can be computed from a crossing point between a minimal geometrical object, in which all separable states reside in the presence of Bloch vectors, and a straight line, which connects the point corresponding to the correlation vector of ρ and the nearest vertex of the maximal tetrahedron, where all two-qubit states reside. It is shown, however, that these properties are not maintained for the arbitrary two-qubit states.