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Two circles (Posted on 2004-10-21) Difficulty: 3 of 5
In a 8½x11 sheet of paper I drew two equal non-overlapping circles -- both completely inside the paper, of course.

What's the largest portion of the paper I could cover with the circles?

What would be the answer if I drew THREE equal circles?

No Solution Yet Submitted by Federico Kereki    
Rating: 3.2500 (4 votes)

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solution | Comment 10 of 11 |

In a rectangle of sides 8.5 cm and 11 cm, the two largest equal non-overlapping circles will have radius = 2.912 cm. The circles will touch each other and one will touch the top and right side of the rectangle and the other will touch the bottom and the left side of the rectangle. Thus the area of the two circles is 53.228 cm². This is the largest portion of the rectangle which can be covered with the help of two equal non-overlapping circles.

If three circles of equal radius are drawn then there radius is equal to 2.278 cm. The largest area that could be covered with the help of these three circles is 48.9275 cm².

  Posted by akash on 2006-01-05 02:18:55
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