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Examples, solutions, videos, worksheets, games and activities to help Geometry students learn how to construct the circumcenter of a triangle.

What is the circumcenter of a triangle?

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.

The following diagrams show the circumcenters for an acute triangle, a right triangle, and an obtuse triangle. Scroll down the page for more examples and solutions on the circumcenters of triangles. How to construct the circumcenter of an acute triangle, a right triangle and an obtuse angle?
Construct Circumcenter of an Acute Triangle

The circumcenter of an acute triangle is located inside the triangle.

Construct Circumcenter of a Right Triangle

The circumcenter of a right triangle is at the midpoint of the hypotenuse.

Construct Circumcenter of an Obtuse Triangle

The circumcenter of an obtuse triangle is outside the triangle opposite the obtuse angle.

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