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Two Semicircles (Posted on 2007-04-27) Difficulty: 3 of 5
A circular disk can be cut into two semicircular pieces easily by cutting along a diameter.

Can the disk be cut into pieces which can be arranged into two semicircles, with none of the cuts passing through the center?

See The Solution Submitted by Brian Smith    
Rating: 2.3333 (3 votes)

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Solution Prior to reading other responses | Comment 4 of 5 |

                 *A*
        *         |          *
      M--J--S--X--U-----N
     *    |   |        |       *
     *    |   |  C    |       *
     *    |   |        |       *
      O--K--T--Y--V-----P
        *          |         *
                  *B*


AB is a diagonal which is intersected by a pair of parallel lines, MN and OP at X and Y, and are equidistant from centre C.

ST and UV are a pair of parallel lines equidistant from and parallel to AB.

JK is parallel to ST with JS = SX.

Cut along all lines and on reassembly J occupies the position of X and X occupies J's original position.

 The construction creates a rectangle whose area is the sum of two smaller rectangles having areas in the ratio of 1:2.
    

Edited on April 27, 2007, 10:25 pm
  Posted by brianjn on 2007-04-27 22:22:11

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