# Tempting Circle

Geometry Level 2

In a circle with center $$O$$, a chord $$AB$$ is drawn such that $$\angle AOB = 120^\circ$$. Radius $$AO=10$$. A circle is drawn in the major arc such that it's radius is maximum, with center E, it touches the larger circle at point X as shown in figure.

The area of the shaded region can be expressed as $$\dfrac{a\pi +b\sqrt{3}}{c}$$ for integers $$a,b,c$$ with $$\gcd(a,c)=1$$ What is the value of $$a+b+c$$?

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