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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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Solution Geometric construction | Comment 12 of 15 |
Construct a 6th circle (of the same radius as the others) to the right of the top two so that its circumference touches the righthand circle, and its centre is collinear with the their centres. Call this centre B.

Extend a straight line from B through A to pass through the circle at A.

Dismissing the newly created 6th circle, There is an area of 2.5 circles above as well as below the line.





  Posted by brianjn on 2006-08-26 19:31:50
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