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Covering A Circle (Posted on 2005-10-21) Difficulty: 3 of 5
A circle of unit radius is completely covered by three identical squares. What is the smallest size of the squares?

See The Solution Submitted by Brian Smith    
Rating: 3.3333 (6 votes)

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Solution non-overlap solution | Comment 2 of 11 |

Let two of the squares share an edge and the third centered above them, sharing half an ege with each.

  +---+

a| d |b
+-+-+-+-+
| o |
+---+---+
c

The circle is centered on the edge shared by the first two squares (o).  3 points on its perimeter are the bottom edge (c)and the two bottom corners of the top square (a and b).  d is the top edge of the bottom squares.

Call the square size x.  We have right triangle ado with
ad=x/2
do=1-x
ao=1

Pythagorean thm. gives (x-1)^2 + (x/2)^2 = 1
Solving gives x=0 or x=1.6



  Posted by Jer on 2005-10-21 12:59:52
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