Here you can see a triangle and the three perpendicular bisector of the sides. The three perpendicular bisectors meet in a single point, the triangle's circumcenter; this point is the center of the circumcircle or circumscribed circle, the circle passing through all three vertices.
You can move the three vertices and watch what happens to the circumcenter.
When you move some of the vertices the circumcenter and the circumcircle change, but the points where the circumcircle touch the triangle are always the same, what are their names?
Celia Díaz, Created with GeoGebra