Circumcenter Exploration
A Grade 10 Math worksheet focusing on understanding and constructing the circumcenter of a triangle, including its properties and applications.
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Circumcenter Exploration
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Read each question carefully and answer to the best of your ability. Show all your work for construction problems.
1. What is the circumcenter of a triangle? What lines intersect to form it?
2. The circumcenter is equidistant from which parts of the triangle?
The midpoints of the sides
The vertices of the triangle
The sides of the triangle
The altitudes of the triangle
3. Construct the circumcenter of the triangle below using only a compass and straightedge. Label the circumcenter 'C'.
4. For an acute triangle, the circumcenter lies the triangle.
5. For an obtuse triangle, the circumcenter lies the triangle.
6. For a right triangle, the circumcenter lies the triangle.
7. A triangle has vertices at A(0,0), B(6,0), and C(3,4). Plot these points on the coordinate plane and find the coordinates of its circumcenter.
Show your work for finding the perpendicular bisectors: