Circumcenter of a Triangle
Explore the properties and construction of the circumcenter of a triangle with this Grade 11 geometry worksheet.
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Circumcenter of a Triangle
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Read each question carefully and answer to the best of your ability. Show all work where applicable.
1. What is the definition of the circumcenter of a triangle?
The intersection of the medians.
The intersection of the angle bisectors.
The intersection of the altitudes.
The intersection of the perpendicular bisectors of the sides.
2. For which type of triangle does the circumcenter lie outside the triangle?
Acute triangle
Right triangle
Obtuse triangle
Equilateral triangle
3. The circumcenter is equidistant from all three of the triangle.
4. The circle that passes through all three vertices of a triangle is called the circle.
5. Consider a triangle with vertices A(0,0), B(4,0), and C(2,6). Find the coordinates of the circumcenter of this triangle.
6. Explain the relationship between the circumcenter and the circumcircle of a triangle.
7. The circumcenter of an acute triangle always lies inside the triangle.
True
False
8. For a right triangle, the circumcenter is the midpoint of the hypotenuse.
True
False