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Math Help - Circles within a square

  1. #1
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    Lightbulb Circles within a square



    This is part c) of a problem using circles within squares - the first 2 parts included information necessary for part c), which included the length of the rope if the total area "eatable" was 288m^2. However, I don't know how to approach this part of the question. Please help! Thanks
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  2. #2
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    circles in square

    Quote Originally Posted by BG5965 View Post


    This is part c) of a problem using circles within squares - the first 2 parts included information necessary for part c), which included the length of the rope if the total area "eatable" was 288m^2. However, I don't know how to approach this part of the question. Please help! Thanks
    Hello BG,
    I think this problem belongs in trig. If you can handle geometry I can help by telling you i calculated the sector angle common to the two goats 55.2 deg. Rest is geometry.

    bjh
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  3. #3
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    Well, removing the goats and company out of there, you've got
    2 intersecting circles, one with center (0,24) and radius 19.15 [1],
    the other with center (24,0) and radius 19.15 [2].
    Their equations are:
    (x - 0)^2 + (y - 24)^2 = 19.15^2 [1]
    (x - 24)^2 + (y - 0)^2 = 19.15^2 [2]

    Now you can easily (easily enough!) calculate the 2 intersecting points...
    Get my drift?
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  4. #4
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    Thanks all of your for your input, I've worked it out now.

    Let the 4 corners be A, B, C, D and and the obtuse angles of the rhombus as E and F.

    By pythagoras, the diagonal is 33.94m, and the 2 radii from either circle (length 19.15m) make a triangle with those dimensions. By cosine rule, the obtuse angle AED is 124.79 degrees, and as opposite angles are equal, so is the other side.

    Therefore, each acute angle is 55.21 degrees, so the area of the sector EDF is 176.69m^2. Similarly, the area of the triangle EDF is 150.59m^2, therefore the extra circular area in the sector is equal to 26.1m^2, which is half of the shared area, so the total shared area is 52.2m^2.

    Once again, thanks a lot for your help BG
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  5. #5
    Junior Member slovakiamaths's Avatar
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    diff. ans

    Dear BG5965, i worked out a diff. ans of your problem. Please check the attachment and give remarks
    Attached Files Attached Files
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  6. #6
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    Quote Originally Posted by slovakiamaths View Post
    Dear BG5965, i worked out a diff. ans of your problem. Please check the attachment and give remarks
    Hi slovakiamaths,

    The answers given by BG5965 are correct. Area in question consists of two back-back circular segments.No relation to ellipse.


    bjh
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