I came across this question in my class:
There are 11 different points in the plane with no 3 points are on the same line.
a) How many circles do these points define? (Points define a circle if there is a unique circle through those points.)
b) How many circles would they define, if 4 points were on the same line?
I think, that we just need 2 points, to define a circle (one for the centre and 1 for the radius). In that case a) would be $11\times10=110$ different circles, however that seems to be incorrect.
How would you solve it?