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Circumscribed Circle of a Triangle

Circumscribed Circle of a Triangle
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2012-07-22 22:48
TriangleCircle
This example demonstrates how to construct the circumscribed circle of a triangle. Key mathematical concepts include triangles and circles. Using GeoGebra commands such as Segment, Polygon, and Circle, the construction of the circumscribed circle is illustrated. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Segment(C, B) → c
  4. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  5. Angle(C, B, A) → α
  6. Angle(B, A, C) → β
  7. Angle(A, C, B) → γ
  8. Midpoint(A, B) → D
  9. Midpoint(B, C) → E
  10. Midpoint(C, A) → F
  11. OrthogonalLine(D, a) → d
  12. OrthogonalLine(F, b) → e
  13. OrthogonalLine(E, c) → f
  14. Intersect(d, e) → M
  15. Circle(M, B) → g

AI Drawing Prompt Reference

Draw a triangle and find the perpendicular bisectors of its three sides. The intersection point of these bisectors is the circumcenter. Draw a circle with this point as the center and radius equal to the distance to any vertex of the triangle, which is the circumcircle of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.