Circumscribed circle (circumcircle) of a triangle
The center of a circumcircle of a triangle is given by interception of the axes of sides.
If we don’t know any angles of the triangle we can use this:
The center of the inscribed ciricle of a triangle is also called incenter. The incenter is the interception of angle bisectors in a triangle.
There are these relations:
Every triangle has three excircle, The center of an excircle is given by interception of angle bisector of internal opposite angle, and the angle bisectors of adjacent external angles.