Circumcenter

The circumcenter of a triangle is the point equidistant from its three vertices, where the perpendicular bisectors of its sides meet.

Perpendicular bisector: A line that passes through a segment’s midpoint at a right angle. The three perpendicular bisectors intersect at the circumcenter.
Triangle: A polygon with three sides and three interior angles. The circumcenter is defined from a triangle’s three vertices.
Compass and straightedge construction: A geometric construction using only an unmarked straightedge and a compass. Intersecting two constructed perpendicular bisectors locates the circumcenter.
Incenter: The point equidistant from a triangle’s sides where its internal angle bisectors meet. Unlike the circumcenter, it is equidistant from sides rather than vertices.
Circumradius: The radius of a circle passing through all vertices of a polygon. Its distance from the circumcenter to any triangle vertex defines this radius.
Vertex (geometry): A point where two or more lines or edges meet. The three vertices are the points equidistant from the circumcenter.
Trilateration: A method for locating a point from its distances to three known points. Three vertex distances can determine a circumcenter when the vertices are known.
Centroid: The intersection of a triangle’s medians, located two-thirds of the way from each vertex to the opposite midpoint. It is determined by medians and vertex averages, not perpendicular bisectors.
Circumcircle: The circle passing through every vertex of a polygon. The circumcenter is the center of a triangle’s circumcircle.
Distance: The length of the shortest straight path between two points. Equal distances from the circumcenter to the vertices establish its defining property.

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