Comments on: How do you prove that the area of a circle circumscribed about a square is twice the area…? http://www.thearealist.com/circle-area/how-do-you-prove-that-the-area-of-a-circle-circumscribed-about-a-square-is-twice-the-area Fri, 03 Feb 2012 13:07:59 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: C Dawg http://www.thearealist.com/circle-area/how-do-you-prove-that-the-area-of-a-circle-circumscribed-about-a-square-is-twice-the-area/comment-page-1#comment-1983 C Dawg Thu, 11 Mar 2010 07:14:59 +0000 http://www.thearealist.com/circle-area/how-do-you-prove-that-the-area-of-a-circle-circumscribed-about-a-square-is-twice-the-area#comment-1983 E.g. AOC=2 Square it and divide by 2 then add 2 due to AOC and you have proven it<br><b>References : </b><br> E.g. AOC=2 Square it and divide by 2 then add 2 due to AOC and you have proven it
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]]> By: Razz http://www.thearealist.com/circle-area/how-do-you-prove-that-the-area-of-a-circle-circumscribed-about-a-square-is-twice-the-area/comment-page-1#comment-1982 Razz Thu, 11 Mar 2010 06:55:59 +0000 http://www.thearealist.com/circle-area/how-do-you-prove-that-the-area-of-a-circle-circumscribed-about-a-square-is-twice-the-area#comment-1982 Let s = the length of the side of a square. Then the area of a circle inscribed in the square = (pi s^2)/4; in this case s is the diameter of the circle. The diagonal of the square is s sqrt(2) A circle circumscribed about the square would have this diagonal as its diameter. Its area would be [pi (s sqrt(2))^2]/4 = [pi x 2s^2]/4 This will be a lot easier to understand if you copy it out in standard math notation; wish we could use equation editor on here) Good luck!<br><b>References : </b><br> Let s = the length of the side of a square.
Then the area of a circle inscribed in the square = (pi s^2)/4; in this case s is the diameter of the circle.

The diagonal of the square is s sqrt(2)

A circle circumscribed about the square would have this diagonal as its diameter.

Its area would be [pi (s sqrt(2))^2]/4 = [pi x 2s^2]/4

This will be a lot easier to understand if you copy it out in standard math notation; wish we could use equation editor on here)

Good luck!
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