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

$$\displaystyle xy^{2}$$

×