Consider the region R = {(x,y) ∈ ℝ × ℝ : x ≥ 0 and y² ≤ 4 − x}. Let ℱ be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles in ℱ. Let (α,β) be a point where the circle C meets the curve y² = 4 − x.
The value of α is ___.