 # Construct the Circumcenter of a Triangle

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High School Math based on the topics required for the Regents Exam conducted by NYSED.

The circumcenter of a triangle is the point where the perpendicular bisectors of each side of the triangle intersect. It can be in the interior or the exterior of the triangle.

The following diagram shows how to construct the circumcenter of a triangle. Scroll down the page for more examples and solutions. Find the Circumcenter of a Triangle
How to construct the circumcenter of a triangle by constructing perpendicular bisectors of each side?
The construction uses only a compass and straight edge.

Constructing the Circumcenter
The point of concurrency of the three perpendicular bisectors of a triangle is the circumcenter. It is the center of the circle circumscribed about the triangle, making the circumcenter equidistant from the three vertices of the triangle. The circumcenter is not always within the triangle. In a coordinate plane, to find the circumcenter we first find the equation of two perpendicular bisectors of the sides and solve the system of equations.
Constructing the Circumcenter of an Acute Triangle Construction (Circumcenter - Obtuse Triangle) Constructing the Circumcircle of a Right Triangle
Construction of the circumcircle of a right triangle, in which it is seen that the circumcenter lies at the midpoint of the hypotenuse.

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