P is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that ∠ACP=120∘. If AC=16 and AP=19, then the radius of Γ can be expressed as a√b/c where b is an integer not divisible by the square of any prime and a,c are

Question

P is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that ∠ACP=120∘. If AC=16 and AP=19, then the radius of Γ can be expressed as a√b/c where b is an integer not divisible by the square of any prime and a,c are 
coprime positive integers. What is a+b+c?