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Circumcenter and Circumcircle of a Triangle by shane molloy

Circumcenter and Circumcircle of a Triangle by shane molloy
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2014-04-14 02:59
TriangleCircleCoordinate Geometry
In collections GCSE Higher Ch8 Transformations & Constructions
This example demonstrates the circumcenter and circumcircle of a triangle. The circumcenter is the intersection of the perpendicular bisectors of the triangle's sides, and the circumcircle is the circle passing through the triangle's vertices. Using GeoGebra commands Polygon, LineBisector, Intersect, and Circle, the circumcircle of any triangle can be constructed. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. LineBisector(A, C) → d
  3. LineBisector(C, B) → e
  4. Intersect(d, e) → D
  5. Circle(D, B) → f

AI Drawing Prompt Reference

Draw an arbitrary triangle. Construct the perpendicular bisectors of two of its sides; these two lines intersect at a point, which is the circumcenter. Using this circumcenter as the center and the distance from it to any vertex as the radius, draw a circle that passes through all three vertices of the triangle, known as the circumcircle. The figure should include the triangle, the two perpendicular bisectors, the circumcenter point, and the circumcircle.
The prompt above was compiled from the original drawing commands and is for reference only.