All $\binom{6}{3}=20$ triples of points can produce distinct circles aside from the case where the three points are collinear $(B D C, C E A, A F B)$.
Let $A B C$ be a triangle and $D, E$, and $F$ be the midpoints of sides $B C, C A$, and $A B$ respectively. What is the maximum number of circles which pass through at least 3 of these 6 points?