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Math Help - A semi-circle in a square.

  1. #1
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    A semi-circle in a square.

    What is the radius of the circle in terms of the edge length of the square?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Natasha1
    What is the radius of the circle in terms of the edge length of the square?
    Draw in the rest of the circle, it will pass through the corner of the square
    as shown in the diagram (a point from which the diameter of a circle
    subtends a right angle is on the circle).

    We can see from the diagram that the diagonal of the square is:

    <br />
r+\sqrt{2 r^2}<br />
,

    now if the side of the square is s the diagonal is:

    <br />
\sqrt{2 s^2}=r+\sqrt{2 r^2}<br />
,

    from which you can finish the problem.

    RonL
    Attached Thumbnails Attached Thumbnails A semi-circle in a square.-wire.jpg  
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  3. #3
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    Lovely solution, Captain Black!
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Soroban
    Lovely solution, Captain Black!
    Thank you.

    RonL
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