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Perpendicular Bisectors of Sides of a Triangle

Perpendicular Bisectors of Sides of a Triangle
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2020-06-03 23:46
TriangleCircleGeometric Construction
This example demonstrates the properties and construction of the perpendicular bisectors of the sides of a triangle. It involves core mathematical concepts such as perpendicular bisectors, midpoints, circumcircle, and geometric transformations. The construction uses commands like Segment, Rotate, Angle, Midpoint, OrthogonalLine, Intersect, and Circle in GeoGebra. Suitable for high school mathematics education or for geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, α, A) → C
  3. Angle(B, A, C) → β
  4. Segment(A, C) → b
  5. Segment(C, B) → c
  6. Midpoint(A, B) → D
  7. OrthogonalLine(D, a) → d
  8. Midpoint(C, B) → E
  9. OrthogonalLine(E, c) → e
  10. Midpoint(C, A) → F
  11. OrthogonalLine(F, b) → f
  12. Intersect(d, e) → O
  13. Circle(O, C) → g

AI Drawing Prompt Reference

Draw a triangle and construct the perpendicular bisectors of each side. Find the intersection points of these bisectors. Use one of the intersection points as the center and one vertex of the triangle as the radius to draw a circle, which should pass through the other two vertices of the triangle, forming the circumcircle.
The prompt above was compiled from the original drawing commands and is for reference only.