Equilateral triangle ABC has a circumcircle Γ with center O and circumradius 10. Another circle Γ1 is drawn inside Γ such that it is tangential to radii OC and OB and circle Γ. The radius of Γ1 can be expressed in the form ab√−c, where a,b and c are positive integers, and b is not divisible by the square of any prime. What is the value of a+b+c?
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