The term circumcenter is a qualifying adjective that is used to designate a point within a more or less complex geometric figure. The circumcenter point can appear in any type of geometric figure that complies with the rules to be explained since it is an imaginary trace that is made on some point of its space or surface. To understand what a circumcenter point is, we must first establish some important elements prior to its formation.
When we talk about geometry, we talk about flat shapes that have different surfaces: triangles, rectangles, quadrilaterals of various kinds, etc. All these shapes have a certain perimeter that is established through the conjunction of lines at a point. To begin, we must establish a circumscribed circumference around the surface or the perimeter of that geometric shape in question, for example a triangle. To be considered circumscribed, this circumference must pass through all the points or vertices of the figure, touching them in its path and completely containing the geometric figure, that is, being larger in terms of surface.
Once we have established what is the circumscribed circumference of a given geometric figure, such as the triangle seen in the image, we can then establish the circumcenter. The circumcenter will be the internal point of the circumscribed circle at which all the lines that may cross it meet and which would otherwise be the point from which the radius and diameter of a circumference or circle are established. To mark the circumcenter point we must vary the technique depending on the figure we have, so for example in a triangle the circumcenter will be given by the union of the three bisectors that form the triangle. To confirm that this circumcenter point is indeed well traced, we must check that it is at the same time the midpoint or central point of the circle previously traced around the figure. In the case of quadrilaterals, the plot of the circumcenter point can be obtained in some cases by marking lines between the vertices whose point of union will be the circumcenter.
