Three point theorem_Star-Delta conversion...Nightmare in circuit solving

As mentioned in the title, this topic is a nightmare when doing circuit solving.

I like to solve circuits a lot. I have done a lot of circuit solving. Everything will go so smoothly as we forget ourselves in the flow until the point we encounter something like below.

The circuit is neither series nor parallel. Struck. That's it. Curious to find out the way to solve the circuit, after doing a lot of searches, I came across the long-forgotten theorem called Start-Delta and Delta-Star conversion. Yup, true I forget this theorem exist at all. I remember that I studied this in Circuit Theorem subject and also remember I have done lot of circuit solving that time. But when it needed, as usual it become long-forgetten.

Coming back to topic, to make the circuit either in series combo or parellel combo, we use this theorem.

The circuits conversion will look like below image.

If we see closely, all three connections in the image are end up as same. Thus why it can be called to many names: Star-Delta conversion, Pi-T conversion and Triangle-Star converison. Its all about the perception. In electronics, Perception of circuit plays very important role. We can call it as mental frameork or mental models.

Lets go into the our favourite part. Solving equation.

Pi-T Conversion:

T-PI Converison:

Now I am planning to create the Math Equation where we will provide value of the resistor and it will automatically covert to its equivlent. Lets go.

Done...

While changine the values in yellow boxes, the values in Green boxes get updated automatically.

If we do the same thing for T-Pi conversion.

Finally its done...While doing this, I observed one thing. Let say in Delta or Pi, RA=RB=RC, then value of resistors in T or star will be, R1=R2=R3=RA/3.

Same way if the resistor value of T or Star is equal, I.e R1=R2=R3, then the values of resistor in Delta is nothing but RA=RB=RC=3xR1. Nice right...