Question: Let S = {(x, y) : x 2 + (y 1) 2 1} {(3, 0)}. Is the origin an extreme point of

Let S =  {(x, y) : x2 + (y – 1)2 ≤ 1} ∪  {(3, 0)}. Is the origin an extreme point of conv S? Is the origin a vertex of conv S?

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