# Outside Fun

Geometry Level 5

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

×