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circumcenter
This term is a technical geometric descriptor used exclusively within the context of Euclidean geometry. It describes a specific point of concurrency, distinguishing it from other triangle centers such as the incenter, centroid, or orthocenter.
Because it is a specialized mathematical term, it is used in a formal, academic register. It is almost always paired with the concept of the circumcircle, as the circumcenter serves as the equidistant point from all three vertices of the triangle.
Meanings
Examples
The circumcenter is the point where the three perpendicular bisectors of a triangle meet.
For an obtuse triangle, the circumcenter lies outside the triangle.
I need to find the coordinates of the circumcenter to draw the circle.
Wait, does the circumcenter always coincide with the centroid in an equilateral triangle?
The distance from the circumcenter to any vertex is equal to the circumradius.
In a right triangle, the circumcenter is located at the midpoint of the hypotenuse.
Let us denote the circumcenter as point O for this proof.
I wonder if there is a faster way to calculate the circumcenter using vectors.