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Math Help - [SOLVED] I Have a Circle inside a Square, and I am asked to find a length

  1. #1
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    [SOLVED] I Have a Circle inside a Square, and I am asked to find a length

    I have a square ABCD, with lengths 8cm
    I have a circle inside the square, as big as it can possibly be, touching all sides. Radius 4cm
    There is a diagonal of the square, passing through the circle.
    Where the diagonal touches the circle, it is called P.

    What I need to do, is prove that AP is equal to 1.66cm

    How do I do this?
    Thanks
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  2. #2
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    4\sqrt 2  - 4 \approx 1.66
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  3. #3
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    let point O be the circle's center.

    OP is a radius = 4

    OA is a leg of the right isosceles triangle \Delta AOB.

    since |AB| = 8 , |OA| = 4\sqrt{2}

    |AP| = |OA| - |OP|
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  4. #4
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    The diagonal d of a square with length s is given by the equation:

    d=s\sqrt{2}

    Does this help you get started?
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    Thanks a lot guys, that was really helpful

    One more question, if it asks me to find DP, how would I get started?
    Would I draw a triangle?
    If so, how where do i go from there?
    Thanks a lot, as you can see, circles are not my strong point
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Ben77mc View Post
    Thanks a lot guys, that was really helpful

    One more question, if it asks me to find DP, how would I get started?
    Would I draw a triangle?
    If so, how where do i go from there?
    Thanks a lot, as you can see, circles are not my strong point
    Hint: use the law of cosines. angle DAP = 45 degrees
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