Why does eutectic point have three phases, but consolute point have only two phases? At eutectic point, there are three phases: solid A, solid B and homogenous liquid phase containing both A and B. 

But at consolute point, we are told it has 2 phases: liquid A and liquid B. 

Why isn't there a homogenous phase containing both liquid A and B at consolute point just like an eutectic point?
I just realised, the 2 phases present in a liquid-liquid solution system with temperature below its solution temperature is a) conjugate solution enriched in A
b) conjugate solution enriched in B

No pure liquid A or pure liquid B phase exists.