Hi everyone. Thanks in advance for your help. I've been working on this problem that is in my analysis book and I'm not sure how to go about it.(adsbygoogle = window.adsbygoogle || []).push({});

I'm required to find the supremum of the epsilon neighborhood around the point (3, 5/2) such that the entire neighborhood is contained is the set S = {the closed triangle with vertices (2,0), (2,2), (4,4)}.

Just so that non-analysis acquainted people can still help me: the epsilon neighborhood that they are asking for is basically a circle with some radius epsilon. They want me to find this radius, I think.

So I thought about taking the equation of the sphere around this point (3, 5/2) and finding where it intersects each of the sides (using the equation of a line), but I ended up going nowhere with this. I was going to take the derivative and find the max or something... I just got lost.

I was also thinking about the idea that the circle would be tangent to one of these lines at the point where the radius is perpendicular to that side of the triangle. So I found the equation of a couple of the lines and took the negative reciprocal, and set those equal to the sphere equation, but that didn't work either! Please help me. Thanks :)

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# Homework Help: An analysis/geometry problem

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