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This oval is made up of 4 arcs, 2 on the left and right sides of radius 1 and 2 on top and bottom of radius $R$. Given that the the oval fits in a $4 \times 8$ rectangle, is it possible to find $R$ ?

oval in rectangle

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    Wait, what radius? Ellipses don't have radii...2011-12-06
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    @J.M.: The question is about ovals, not ellipses. Ovals are actually constructed from pairs of arcs.2011-12-06
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    @Heike: So the title has deceived me, I presume... I have no love for titles not agreeing with post bodies.2011-12-06
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    If Heike's interpretation of the question is the intended one, you should replace "ellipse" by "oval" and "arcs" by "circular arcs". Also, if I understand Heike's solution correctly, it assumes continuous tangents at the transition points. If this is supposed to be part of the problem statement, you should explicate it.2011-12-06
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    @J.M.: Sorry, I missed the title. I agree that mentioning ellipse in the title is misleading.2011-12-06
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    @joriki: I assumed that the O.P. wanted a smooth curve. I probably should have mentioned that in my solution.2011-12-06
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    @Heike: The curve isn't smooth in the technical sense, only $C^1$.2011-12-06

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