Can't understand solution on Rohith and Circles problem from July Challenge

I am struggling with this solution for Rohith and Circles problem. Particularly, I do not understand where the line yl=(.25*((1.0/r4)-(1.0/r3)))-rs; comes from. (This is the y-coordinate of leftmost circle after transformation).

Maybe someone can help me to figure out this? Thanks.

is it possible to contact author via codechef? namely @vijay_cipher.

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