Let ABCD be a square of side of unit length. Let a circle C_1 cantered at A with unit radius is d...

Let ABCD be a square of side of unit length. Let a circle C_1 cantered at A with unit radius is drawn. Another circle C_2 which touches C_1 and the lines A D and A B are tangent to it, is also drawn. Let a tangent line from the point C to the circle C_2 meet the side A B at E. If the length of EB is α+√(3)β, where α, β are integers, then α+β is equal to

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