Geometric race line - 90 degree angular curve

Question

I am in a process of solving the race curve by driving from outside to inside for $90˚$ curves. I'm trying to solve it with Pythagoras but somehow my theory seems to be flawed. Wolfphram alpha gives error and my calculator seems to give very low results for R2:

This gives:

$$(R2-R1)^2 = (R2-R1-W)^2 + (R2-R1-W)^2$$

I know there is another solution on this website, but I would like to know where I am wrong.

Thanks in advance!

Answer 1

Ok so you should have

$\begin{align*} (R_2-R_1)^2&=2(R_2-R_1-W)^2\\R_2-R_1&=\sqrt2(R_2-R_1-W)\\0&=(\sqrt2-1)(R_2-R_1)-\sqrt2W\\R_2&=R_1+\frac{\sqrt2}{\sqrt2-1}W\end{align*}$