# Thread: Two circles and a square

1. ## Two circles and a square

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?

2. 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!

3. I get 18.

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