Let A be a closed, convex subset of R^{k} and let c = (c1,...,ck) be a point disjoint of A in R^{k}. [R is reals]

Then by Second Geometric Form of Hahn-Banach Theorem we can strictly separate A and {c}
by a hyperplane.

How do we show that we can always find a point b = (b1,...,bk) in R^{k}
and an alpha in R such that:

b.a < alpha < b.c for all a in A (. is dot product)

Thanks for any assistance!