Outside Fun

Geometry Level 5

The three blue circles with centers X,YX, Y and ZZ are each tangent to two of the lines making up the triangle ABCABC and each of them has twice the area of the incircle of the triangle ABCABC. If the area of the triangle ABCABC is 1, find the area of the triangle XYZXYZ and express it as a+bca+b\sqrt{c}, where a,ba,b and cc are positive integers with c1c \neq 1 square-free. Submit your answer as a+b+ca+b+c.

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