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        *                 *                 *
 *               * *               * *               *
  *             *   *             *   *             *
    *         *       *         *       *         *
         *                 *                 *
       
      

(In reply to re(3): Equation spoiler by Richard)

With point A at (0,0), the point (3,1) is only a point on the line (or line segment) that divides the five circles into two halves.  It has no more importance than the point (1/2, 1/6) for identifying the line that divides the five circles.  I asked the question about the points of the line segment to try to hint that any line segment that did not extend from point B [which would lie in quadrant III and on the circle with midpoint A, and thus be in the form (-x, -y)] to C [which would be on the second circle of the top circles in quadrant I] or to points beyond was too short of a line segment to divide the five circles in half. 

Posted by Dej Mar on 2006-08-26 19:48:09