SOLUTION: what are the largest two circles that will fit in a square 2ft. x 2ft. ?
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Question 995585: what are the largest two circles that will fit in a square 2ft. x 2ft. ?
marbles@ptd.net
Answer by ikleyn(52914) (Show Source): You can put this solution on YOUR website!
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what are the largest two circles that will fit in a square 2ft. x 2ft. ?
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The problem was formulated inaccurately.
The circles should have the same radius, isn't it?
Why do not say it explicitly?
It is better to formulate the problem like this:
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You want to cut two circles of the same radius from the square of 2 ft. x 2 ft. Find the maximal possible radius.
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I think what you will get the maximal possible radius if you place the centers of circles in the square's diagonal. Let us accept it without proof.
Then you have this equation for the radius of the circles:
+ + = ,
where a is the measure of the square's side.
Therefore, r = .
r = = = 0.586 ft (approximately).
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