Circumcenter Exploration Worksheet
Explore the properties and construction of the circumcenter of a triangle with this grade 9 geometry worksheet.
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Circumcenter Exploration Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for construction problems.
1. The circumcenter of a triangle is the point where the of the sides intersect.
2. The circumcenter is equidistant from the three of the triangle.
3. The circle that passes through all three vertices of a triangle is called the .
4. For which type of triangle does the circumcenter lie outside the triangle?
Acute triangle
Right triangle
Obtuse triangle
Equilateral triangle
5. Where does the circumcenter of a right triangle lie?
Inside the triangle
Outside the triangle
On the hypotenuse
On one of the legs
6. Construct the circumcenter of the triangle below. Label the circumcenter 'C' and draw the circumcircle.
7. The circumcenter is always inside an acute triangle.
True
False
8. The circumcenter is the center of the inscribed circle.
True
False
9. A triangle has vertices at A(1,1), B(5,1), and C(3,5). Plot these points on the graph below. Then, find the coordinates of the circumcenter and explain your method.