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Circumcircle of a Triangle

Circumcircle of a Triangle
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2019-10-09 01:53
TriangleCircleGeometric Construction
This example demonstrates how to construct the circumcircle of a triangle by finding the intersection of the perpendicular bisectors of its sides. Key math concepts include midpoints, perpendicular lines, intersections, and circumcircles. GeoGebra commands and objects used are Segment, Midpoint, Line, OrthogonalLine, Intersect, and If. Suitable for middle school and above students to learn basic geometric properties of triangles, ideal for classroom demonstrations and geometric constructions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Midpoint(A, C) → M
  5. Midpoint(C, B) → L
  6. Midpoint(B, A) → N
  7. Line(A, C) → l
  8. Line(C, B) → m
  9. Line(B, A) → n
  10. OrthogonalLine(N, n) → i
  11. OrthogonalLine(M, l) → j
  12. OrthogonalLine(L, m) → k
  13. Intersect(i, j) → O
  14. Intersect(j, m) → D
  15. Intersect(k, l) → E
  16. If(a < 1, Segment[L, (x(L) + (a * (x(E) - x(L))), y(L) + (a * (y(E) - y(L))))], Segment[L, E]) → q
  17. Intersect(m, i) → F
  18. If(2 < a < 3, Segment[N, (x(N) + ((a - 2) * (x(F) - x(N))), y(N) + ((a - 2) * (y(F) - y(N))))], a ≥ 3, Segment[N, F]) → r
  19. If(1 < a < 2, Segment[M, (x(M) + ((a - 1) * (x(D) - x(M))), y(M) + ((a - 1) * (y(D) - y(M))))], a ≥ 2, Segment[M, D]) → p
  20. If(3 < a < 4, Circle[O, (x(O) + ((a - 3) * (x(A) - x(O))), y(O) + ((a - 3) * (y(A) - y(O))))], a ≟ 4, Circle[O, A]) → c

AI Drawing Prompt Reference

Draw a triangle ABC, then find the midpoints M, L, N of sides AB, BC, CA respectively. Draw the perpendicular bisectors i, j, k through these midpoints. The intersection point O of these bisectors is the circumcenter of the triangle. Finally, draw the circumcircle with O as the center and A as the radius.
The prompt above was compiled from the original drawing commands and is for reference only.