Circumcenter of a Triangle
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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.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
More Lessons for Grade 9
Math Worksheets
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.
The circumcenter of a right triangle is at the midpoint of the hypotenuse.
The circumcenter of an obtuse triangle is outside the triangle opposite the obtuse angle.
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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