About convex hull and fixed point

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sapporozoe
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First, I wonder whether I can put the post here...

Given
X=[0,1]^2

a(x)={y in X:||y-x||>=1/4}

b(x)is the convex hull of a(x).

Identify the set of fixed points.

My answer is 3/4>=x>=1/4, 3/4>=y>=1/4, but I am not sure...

What if we have a(x)={y in X:||y-x||>=1/2}? (My answer is x=1/2 or y=1/2)

Thanks.
 
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