Circle Reflection and Arc Length

Let circle C be the image of x² + y² – 2x + 4y – 4 = 0 in the line 2x – 3y + 5 = 0 and A be the point on C such that OA is parallel to x-axis and A lies on the right hand side of the centre O of C. If B(α,β), with β < 4, lies on C such that the length of the arc AB is (1/6)^th of the perimeter of C, then  is equal to