The are 10 points in a plane of which no three points are collinear but 4-points are concyclic. The number of different circles that can be drawn through at least 3 points of these points is

A unique circle can be drawn throw three points, hence a selection of three points results in a circles. So, the maximum number of circles using 10 points is _{${}^{10}{C}_3.$}  Now, out of these 10 points 4 are concyclic, hence _{${}^4{C}_3$}  circles are actually number of circle.

_$\therefore$  Required number of circles _{$={}^{10}{C}_3{-}^4{C}_3+1=117.$}