Kissing Circles For Valentines Day

Geometry Level 2

Two circles of with equal radii are tangent to each other at point CC. Line segment ABAB is tangent to both circles, where AA and BB are the points of tangency.

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

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