How can I show that R and RL are equal in this Y/Delta circuit problem?

[gomezfx]

Homework Statement

[PLAIN]http://img38.imageshack.us/img38/1620/halpwd.jpg

Homework Equations

I've been simplifying the circuit but with no real objective or guidance. I just don't know how to even begin to show that R and RL are equal. Can someone please help me?

The Attempt at a Solution

This is my work so far. I've just tried simplifying it, but like I said I have no real idea what to do next.
http://img706.imageshack.us/img706/6398/imggc.jpg

 

[rl.bhat]

You have already converted Y to Δ.

After simplification, new Δ consists of 3R, 3R/4 and 3R.

Again convert Δ to Y. Three sections contain R/3, R/3 and 4R/3.

So Rab = RL = R/3 + [4R/3*(R/3+RL)]/(R/3 + 4R/3 + RL)

Simplify the equation.

 

[gomezfx]

Wow, thanks a lot!

 

[gomezfx]

Does anyone know how I can get part B?

 

[rl.bhat]

Total current I = vi/R.

Current through c-d branch is

T2 = I*(4R/3)/2*4R/3 = I/2

vo = R*I/2 = vi/2