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Math Help - how can i get largest square in circle

  1. #1
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    how can i get largest square in circle

    i want to get maximum area of square can be drawn in a circle if its diamemter is "d"

    eg:
    7 ---->24.5
    12 ---->72
    29 ---->420.5
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mido22 View Post
    i want to get maximum area of square can be drawn in a circle if its diamemter is "d"

    eg:
    7 ---->24.5
    12 ---->72
    29 ---->420.5
    The largest square in the circle would be one that touches the circle on all four vertices, so the diagonal across the square will be the same as the diameter of the circle...

    -Dan
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  3. #3
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    e^(i*pi)'s Avatar
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    If I understand correctly the diameter will also be the longest diagonal across the square.

    From Pythagoras you know that d^2 = 2a^2 \text{  and  } d = a\sqrt{2} \implies a = \dfrac{d}{\sqrt{2}} where a is the side length.

    (nb: because side length must be greater than 0 I have discarded the negative root)

    Now what do you know about the area of a square?
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  4. #4
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    Quote Originally Posted by e^(i*pi) View Post
    If I understand correctly the diameter will also be the longest diagonal across the square.

    From Pythagoras you know that d^2 = 2a^2 \text{  and  } d = a\sqrt{2} \implies a = \dfrac{d}{\sqrt{2}} where a is the side length.

    (nb: because side length must be greater than 0 I have discarded the negative root)

    Now what do you know about the area of a square?
    thx very much
    the area of square will be : r*r*2
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by mido22 View Post
    thx very much
    the area of square will be : r*r*2
    If you think r is the radius of the circle then NO.

    Read what the others have posted above. The diagonal of the square will be equal to a diameter of the circle.

    So what is the side of a square it its diagonal is d?

    CB
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