Here is a problem from *Five Hundred Mathematical Challenges* that I indeed found quite challenging.

**“Problem 235. **Two fixed points *A* and *B* and a moving point *M *are taken on the circumference of a circle. On the extension of the line segment *AM *a point *N *is taken, outside the circle, so that lengths MN = MB*. *Find the locus of *N.*”

Since one of the first hurdles I faced with this problem was trying to figure out what type of shape was being generated, I thought I would omit my usual drawings illustrating the problem statement. There turned out to be a lot of cases to consider, but the result was most satisfying. I also included the case when *N* is inside the circle. Again Visio was my main tool to handle all the examples with the concomitant requirement to prove whatever Visio suggested.

See the Curve Making Puzzle