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: Equation spoiler by Richard)

With point A at the origin, Larry's equation for the line is correct.

Point B, as it is not in the figure and could be defined as any point of the line, could be at (3,1).  Yet, if point B were to be defined to be a point on the line other than point A, it would be at (3n,1n) where n is a real number other than 0.

A question could be asked, if point A were at origin (0,0) of circle of radius = 1, what are the two points, B and C, on the circles where the line segment BC separates the five circles into areas of equal halves?

Posted by Dej Mar on 2006-08-26 16:02:15