From the Delta Connection:
Resistance among terminals 1 and 2 whereas 3 is open circuited.
Rc and Rb are in series. This combination is in parallel to Ra.
R12 = Ra (Rb + Rc ) / Ra + Rb + Rc
Likewise, the resistances between terminals 2 and 3 and 1 and 3 are given by :
R23= (Ra + Rc ) Rb/ Ra + Rb + Rc
R13 = (Ra + Rb ) Rc / Ra + Rb + Rc
Now compare the results of star and delta connections:
R 1 + R2 = Ra (Rb + Rc )/ Ra + Rb + Rc
R 2 + R3 = Rb (Ra + Rc )/ Ra + Rb + Rc
R 1 + R3 = Rc (Ra + Rb )/ Ra + Rb + Rc
We may determine three unknown resistances Ra, Rb and Rc in terms of R1, R2 and R3.
R a = R1 R2 + R2 R3 + R3 R1/ R3
R b = R1 R2 + R2 R3 + R3 R1/ R1
R c = R1 R2 + R2 R3 + R3 R1 / R2