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Circumcenter Exploration

A circumcenter is the point of concurrency of the three perpendicular bisectors. 1) Triangle XYZ has been constructed for you. 2) Construct the perpendicular bisector of each side using the Toolbar Image tool. for example to bisect side XY, click on the Toolbar Image tool, then click on side XY. 3) Use the intersect Toolbar Imagein the point menu to mark the point where all three perpendicular bisectors meet. Mathematicians call this the circumcenter . Right click this point and rename it A.
Image
Construct the circumcenter below.

Drag the vertices of XYZ around. What kind of triangle is XYZ if the circumcenter A falls on the exterior of the triangle?

选择所有适用项
  • A
  • B
  • C
检查答案 (3)

What kind of triangle is XYZ if the circumcenter A falls on the triangle?

选择所有适用项
  • A
  • B
  • C
检查答案 (3)

What kind of triangle is XYZ if the circumcenter A is in the interior of the triangle?

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  • A
  • B
  • C
检查答案 (3)
A circumscribed circle (circle that goes through each vertex) can be added in this construction above. Use the circle tool (Toolbar Image) to make a circle with the center at the circumcenter (point where all the perp. bisectors meet) and that goes through one of the vertices of the triangle.
Image

Drag around the vertices of XYZ. Does the circle always go through the three vertices and remain outside the triangle?

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  • A
  • B
检查答案 (3)

Since a circumscribed circle goes through each vertex, the circumcenter is equidistant from each:

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  • A
  • B
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