How Many Circles go Through 3 Distinct Points of $\mathbb{R}^2 $

Question

Let $x,y$ and $z$ three distinct points of $\mathbb{R}^2$. How many circles go through these 3 points and what's their centre relatively to $x$,$y$ and $z$?

Answer 1

If all three points are on some straight line, there are no circles going through all three points.

If they are not on one straight line, there is exactly one circle hitting all three point and that is the circumcircle around the triangle $\Delta{xyz}$.