Tempting Circle

Geometry Level 2

In a circle with center OO, a chord ABAB is drawn such that AOB=120\angle AOB = 120^\circ. Radius AO=10AO=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 aπ+b3c\dfrac{a\pi +b\sqrt{3}}{c} for integers a,b,ca,b,c with gcd(a,c)=1\gcd(a,c)=1 What is the value of a+b+ca+b+c?

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