Thread: 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?

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 represent the square and two circles.

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

The maximum number of intersections is: .


Bottom line: is such a figure possible?

Code:

              * * *           * * *
          *           *   *           *
        *               o               *
       *               * *               *

      *               *   *               *
      *         * - - o - o - - *         *
      *         |     *   *     |         *
                |               |
       *        |      * *      |        *
        *       |       o       |       *
          *     |     *   *     |     *
              * o *           * o *
                |               |
                * - - - - - - - *

Yes!

I get 18.

Unless the circles have equal radius and overlay each other,
in which case all of the circle's points intersect.