Kissing Circles For Valentines Day

Geometry Level 2

Two circles of with equal radii are tangent to each other at point \(C\). Line segment \(AB\) is tangent to both circles, where \(A\) and \(B\) are the points of tangency.

Let the area of \(\triangle ABC\) be \(x\) and let the combined area of the circles be \(y\). What is \(\frac{y}{x}\) rounded to 4 decimal places?

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