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Five Circle Division (Posted on 2006-08-26) Difficulty: 2 of 5
Five circles are arranged in the following fashion ( Two rows of 3 circles in square arrangement with one end circle removed from the top row ). Circles are of same diameter and touching adjoining circles as per the diagram. Draw a line passing through A ( Centre of the first circle on the bottom row ) in such a way that it divides the five circles into two equal areas.


                           *                 *
                      *         *       *         *
                    *             *   *             *
                   *               * *               *
                  *                 *                 *
                   *               * *               *
                    *             *   *             *
                      *         *       *         *
         *                 *                 *
    *         *       *         *       *         *
  *             *   *             *   *             *
 *               * *               * *               *
*        A        *                 *                 *
 *               * *               * *               *
  *             *   *             *   *             *
    *         *       *         *       *         *
         *                 *                 *
       
      

No Solution Yet Submitted by Salil    
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re: new question | Comment 9 of 15 |
(In reply to new question by Daniel)

It is obvious that the solution is unique. Any line through A divides the disk X of which A is the center into two equal areas, so your X1 must equal your X2 no matter what line through A is chosen.
  Posted by Richard on 2006-08-26 17:58:00

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