Question 1203324
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If 4 points on the circle determine a rectangle, then there are 2 of those points on each half of the circle.<br>
So the worst case, if you are trying to get a rectangle with the points you choose, is to first pick all 9 points on one half of the circle.  Then any 2 points on the other half of the circle will determine a rectangle.<br>
ANSWER: 9+2 = 11<br>
Note this solution is easier to see by drawing sketches to consider cases with smaller even numbers of point on the circle.<br>
6 points: choose the 3 on one side of the circle; any one 4th point still does not determine a rectangle, but then any 5th point does. 3+2 = 5<br>
8 points: choose the 4 on one side of the circle; any one 5th point still does not determine a rectangle, but then any 6th point does. 4+2 = 6<br>