Let K subset of R^n be a convex set. We call x1 element of K an extreme point of K if K/{x1} is convex too.

Prove that x1 element of K is an extreme point iff cx + (1-c)y = x1 for 0<c<1, c element of R (real numbers as above) implies x = y = x1.

any answer or help will be greatly appreciated.