There are 10 points in a plane of which no three points are collinear and four points are concyclic. The number of different circles that can be drawn through at least three points of these points is

Number of points required for the fixed circle is 3. So, first select any three points from the 10 points in ${ }^{10}{C}_3$ ways.
In these ways, circle with four concyclic points is selected in ${ }^4{C}_3$ ways. But it should be taken once then total number of circles is $\left({ }^{10}{C}_3{-}^4{C}_3\right)+1$.