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GeoGebra

5.1 Circumcenters of Triangles

Autor:Maryann Redelfs
The circumcenter of a triangle is a point of concurrency for the three perpendicular bisectors of the sides of the triangle. In the triangle ABC below, each of the 3 sides has a perpendicular bisector constructed. Modify the construction in order to examine the circumcenter of different triangles and explore the properties of the circumcenter .

Task 1

Modify the shape of the triangle by dragging its vertices with the mouse. Change the measures of the angles, the lengths of the sides, and the location of the circumcenter. Move the vertices in multiple locations to observe changes when...   a) all angles are acute.    b) one angle is obtuse.    c) one angle is a right angle. and then answer the questions below.

Where is the circumcenter when the triangle is acute?

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  • A
  • B
  • C
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Where is the circumcenter when the triangle is obtuse?

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  • A
  • B
  • C
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Where is the circumcenter when the triangle is a right triangle?

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  • A
  • B
  • C
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Can you manipulate the vertices to make one of the perpendicular bisectors intersect a vertex of the triangle? If so, what kind of triangle is created?

Can you manipulate the vertices to make all of the perpendicular bisectors intersect the vertex opposite their side of the triangle? If so, what kind of triangle is created?

The circumcenter is the center of the blue circle. No matter what type of triangle is constructed, what do you notice about the relationship between the blue circle and the vertices of the triangle? What does that tell you about the relationship between the circumcenter and the vertices of the triangle?

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