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Circumcenter of a Triangle by Stephanie Harman Smith

Circumcenter of a Triangle by Stephanie Harman Smith
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2018-02-02 00:36
TriangleCircleGeometric Construction
In collections Geometry Review
This example demonstrates the concept of the circumcenter of a triangle, which is the point where the perpendicular bisectors of the triangle's sides intersect, and also the center of the triangle's circumscribed circle. Using GeoGebra commands such as Polygon, LineBisector, and Intersect, one can construct a triangle and find its circumcenter. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. LineBisector(b) → bisectsAC
  3. LineBisector(c) → bisectsAB
  4. LineBisector(a) → bisectsBC
  5. Intersect(bisectsAC, bisectsAB) → D
  6. Segment(A, D) → AD
  7. Segment(B, D) → BD
  8. Segment(C, D) → CD
  9. Circle(D, A) → Circle

AI Drawing Prompt Reference

Draw a triangle ABC, then construct the perpendicular bisectors of sides BC, CA, and AB, find their intersection point D, which is the circumcenter of triangle ABC, and finally draw a circle centered at D passing through point A.
The prompt above was compiled from the original drawing commands and is for reference only.