Radius Ratio #1

Geometry Level 4

Consider 2 circles of radius a and b ( b > a) both lying in the first quadrant and touching both coordinate axes.

If the 2 circles intersect each other orthogonally

Then \(\frac{b}{a}\) can be written as

\(\displaystyle x + \sqrt{y}\), where 'y' is square free

Then find

\(\displaystyle xy^{2}\)


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