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Consider the region `R = {(x, y) in R xx R : x ge 0 and y^2 le (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 `(alpha, beta)` be a point where the circle `C` meets the curve `y^2 = 4 − x`.
The radius of the circle `C` is ___

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Consider the region R = {(x, y) in R xx R : x ge 0 and y^2 le (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 (alpha, beta) be a point where the circle C meets the curve y^2 = 4 − x . The value of alpha is ___ .

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