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Math Help - circle geometry

  1. #1
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    circle geometry

    1.Two circles are drawn in a 12-inch by 14-inch rectangle. Each circle has a diameter of 6 inches. If the circles do not extend beyond the rectangular region, what is the greatest possible distance between the centers of the circles?

    ** I came up with 8inches just by looking at the word problem, but I dont know how to set it up **



    2. The area of square I is 1 square unit. A diagonal of square I is a side of square II, and a diagonal of square II is a side of square III. What is the area of square III?
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  2. #2
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    2.) We know that the diagonal of a square of side a is \sqrt(2) * a This can come from the Pythagorean Theorem, or Trigonometry.
    So if a = 1, then the diagonal is \sqrt(2). If that square has side \sqrt(2), its diagonal is \sqrt(2) * \sqrt(2) = 2. A square with side 2 has area 4.
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  3. #3
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    Quote Originally Posted by terr13 View Post
    2.) We know that the diagonal of a square of side a is \sqrt(2) * a This can come from the Pythagorean Theorem, or Trigonometry.
    So if a = 1, then the diagonal is \sqrt(2). If that square has side \sqrt(2), its diagonal is \sqrt(2) * \sqrt(2) = 2. A square with side 2 has area 4.

    Terr you totaly lost me on the explanation!
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  4. #4
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    Let's use the coordinate plane.
    Attached Thumbnails Attached Thumbnails circle geometry-untitled-circles.jpg  
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  5. #5
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    The only thing you need for the 2nd one is that the diagonal of a square is \sqrt(2) times its side length.
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