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Math Help - Two circles and a square

  1. #1
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    Two circles and a square

    Please solve this problem. Thanks.


    Two distinct circles and a square lie in the plane. What is the maximum number of points of intersection of two or more of these three figures?
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  2. #2
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    Hello, chil2e!

    Two distinct circles and a square lie in the plane.
    What is the maximum number of points of intersection of 2 or more of these 3 figures?
    We can "talk" our way through most of it.

    Let S, C_1, C_2 represent the square and two circles.

    We can "see" that:
    . . S and C_1 intersect in at most 2 points.
    . . S and C_2 intersect in at most 2 points.
    . . C_1 and C_2 intersect in at most 2 points.

    The maximum number of intersections is: . 2+2+2 \:=\:6


    Bottom line: is such a figure possible?
    Code:
                  * * *           * * *
              *           *   *           *
            *               o               *
           *               * *               *
    
          *               *   *               *
          *         * - - o - o - - *         *
          *         |     *   *     |         *
                    |               |
           *        |      * *      |        *
            *       |       o       |       *
              *     |     *   *     |     *
                  * o *           * o *
                    |               |
                    * - - - - - - - *

    Yes!

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  3. #3
    MHF Contributor
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    I get 18.

    Unless the circles have equal radius and overlay each other,
    in which case all of the circle's points intersect.
    Attached Thumbnails Attached Thumbnails Two circles and a square-scc.jpg  
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