Mathematics · Geometry

Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius be drawn. Another circle C2 which touches C1 externally and the lines AD and AB as tangents is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is α + √3 β, where α, β are integers, then α + β is equal to: