User:Asf
This page is going to be a collection of problems (without solutions from me yet) from a math circle that I go to because I don't know where else to put them.
January 27, 2011
1. Place 4 points on the plane in such a way that every triangle with vertices at these 4 points is isosceles. Could you do the same with 5 points? More than 5 points?
2. Plot 2 points A and B a distance 2 units apart (choose your own unit length).
(a) Place 6 points in such a way that for every point 
of these 6 points, ![\[AP-BP=0,\]](http://latex.artofproblemsolving.com/8/a/1/8a141786a4633d635b9724b0126648f549658d93.png)
i.e. the difference between the distances from P to the two points B is exactly 0.
(b) Place 6 points in such a way that for every point of these 6 points either ![\[AP-BP=1\text{ or }BP-AP=1,\]](http://latex.artofproblemsolving.com/d/7/5/d75a171f634d99c679f4bb97841ba76a477f7576.png)
i.e. the positive difference between the distances from P to the two points A and B is exactly 1.
