SOLUTION: a circle is inscribed in a square and circumscribed about another. detrermine the ratio of the area of the larger square to the area of smaller square.

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Question 1116523: a circle is inscribed in a square and circumscribed about another. detrermine the ratio of the area of the larger square to the area of smaller square.
Found 2 solutions by math_helper, greenestamps:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


The drawing for this situation is:

Let d=diameter of the circle.
The small square has a diagonal length of d, so the sides are +d%2Fsqrt%282%29+ units long.
The large square has sides that are +d+ units long.
So the ratio of large to small is +%28d%5E2%29%2F+%28%28d%5E2%2F2%29%29+=+highlight%28+2+%2F+1+%29++ or +highlight%28+2%3A1+%29+
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What tutor greenestamps says is correct. If one draws the inner square as below, the 2:1 ratio in the areas is much more obvious.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Draw the figure so that the inscribed square has its vertices where the circle is tangent to the circumscribed square.

Then, by drawing the diagonals of the inscribed square, it is easy to see that the ratio of the areas of the two squares is 2:1.