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(2): Equation spoiler by Dej Mar)

Which points?  The line intersects 3 of the circles, each in two points.  Discounting the circle with center A, there are still 4 points where the line intersects the other two circles, 2 for each circle. And why should anyone care what any of those points are? Putting A at (0,0) and giving the circles unit radius, the important point is (3,1).

Posted by Richard on 2006-08-26 18:08:21