The circumcircle of a triangle is the unique circle determined by the three vertices of the triangle. Its center is called the circumcenter (blue point) and is the point where the (blue) perpendicular bisectors of the sides of the triangle intersect.
The incircle of a triangle is the circle inscribed in the triangle. Its center is called the incenter (green point) and is the point where the (green) bisectors of the angles of the triangle intersect.
The incenter and the circumcenter coincide if and only if the triangle is equilateral. Alter the shape of the triangle by dragging the vertices.