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.
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(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 20060826 19:48:09 