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Math Help - SAT Geometry Question

  1. #1
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    SAT Geometry Question

    SAT Geometry Question-photo-9-.jpg

    The part that is cut off is asking the area of the shaded section of the circle. How do I solve this problem only knowing one side of the square?
    Last edited by anthonybjj94; July 17th 2013 at 08:09 AM.
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  2. #2
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    Re: SAT Geometry Question

    there is a problem with your post
    I can't see the problem....
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  3. #3
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    Re: SAT Geometry Question

    Thank you. I will try to remedy this.
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    Re: SAT Geometry Question

    I updated the post.
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  5. #5
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    Re: SAT Geometry Question

    Quote Originally Posted by anthonybjj94 View Post
    Click image for larger version. 

Name:	photo (9).JPG 
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    The part that is cut off is asking the area of the shaded section of the circle. How do I solve this problem only knowing one side of the square?
    The radius of that circle is 1. The angle at O is \tfrac{\pi}{2}.
    Thus the shaded area is \tfrac{1}{4} the area of the circle.
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    Re: SAT Geometry Question

    I understand that the radius is 1, due to the side of the square being the diameter. However, I don't understand how you found O's angle. Can you explain, please?
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    Re: SAT Geometry Question

    Quote Originally Posted by anthonybjj94 View Post
    I don't understand how you found O's angle. Can you explain, please?
    You are expected to know about the diagonals of a square.
    What are the properties of diagonals?
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    Re: SAT Geometry Question

    They are perpendicular, correct?
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    Re: SAT Geometry Question

    and, I believe, make four 45-45-90 triangles, which would mean that the shaded area is 1/4 of the circle.
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    Re: SAT Geometry Question

    A=Pi(D)

    A=Pi(2)/4


    A= Pi/2

    I think I got it!
    Last edited by anthonybjj94; July 17th 2013 at 09:26 AM.
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    Re: SAT Geometry Question

    But I do have an additional question:

    When I plugged in the radius to the formula A=Pi(r)2 I received Pi/4 as an answer. Where did I err?
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    Re: SAT Geometry Question

    Quote Originally Posted by anthonybjj94 View Post
    A=Pi(D)

    A=Pi(2)/4


    A= Pi/2

    I think I got it!
    This is where your error is: C = \pi D, not A.

    -Dan
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  13. #13
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    Re: SAT Geometry Question

    Silly me. As you can see, I am still knocking the rust off. Thank you for all of the help! What you do is admirable!
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