This construction and the equality of chemical potentials results in the common tangent construction between several phases of heterogeneous solution in a binary alloy:
Which allows the construction of binary phase diagrams, for example:
The two phase regions are composed of the limiting compositions on either side of the two-phase region on the phase diagram; the lever rule allows us to determine the fractions of each phase.
There are four main types of binary phase diagrams: Eutectic-type, Peritectic-type, Spinodal, and Lens. You should be able to draw these without too much effort.