I need help with a circle area problem (challenge update)

[kobmat]

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Took a swing at unequal radii thing using what i used for the equal radii thing. And what i got is below. Im not sure though if its correct

[rodsky]

To moz_k2 and kobmat, I cannot thank you enough for your contributions to this thread. Great work and excellent effort in solving the problem. I have to admit that numerical integration and calculus is well beyond my ability to compute and solve problems, but as far as I can follow, your solutions seem to solve the problem at hand. Again, many thanks.

This thread is an excellent example of what can happen if someone posts an innocent enough question, and tap the minds of people who are simply eager to see if the problem can actually be solved. Cooperation is still one of humanity's greatest asset.

-RODION

[batsoy]

how i wish i could turn 4 years back scanning my review books. it's so nice to see beautiful analytical minds here.

[kobmat]

The problem now is how to solve the integral and simplify. Maybe we can find a simple relation between the variables like PO, radius and AoE.