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Incircle of a Triangle

Incircle of a Triangle
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2019-10-09 01:46
TriangleCircleGeometric Construction
This example demonstrates the incircle of a triangle, which is a circle that is tangent to all three sides of the triangle. Key construction steps include using the AngularBisector command to construct angle bisectors, and finding their intersection, which is the center of the incircle. GeoGebra commands used include Segment, AngularBisector, Intersect, etc. Suitable for middle school and above students to learn about triangle properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. AngularBisector(C, A, B) → i
  5. AngularBisector(A, B, C) → j
  6. AngularBisector(B, C, A) → k
  7. Intersect(i, g) → X
  8. Intersect(j, h) → Y
  9. Intersect(k, f) → Z
  10. If(a < 1, Segment[A, (x(A) + (a * (x(X) - x(A))), y(A) + (a * (y(X) - y(A))))], Segment[A, X]) → l
  11. If(2 < a < 3, Segment[C, (x(C) + ((a - 2) * (x(Z) - x(C))), y(C) + ((a - 2) * (y(Z) - y(C))))], a ≥ 3, Segment[C, Z]) → n
  12. If(1 < a < 2, Segment[B, (x(B) + ((a - 1) * (x(Y) - x(B))), y(B) + ((a - 1) * (y(Y) - y(B))))], a ≥ 2, Segment[B, Y]) → m
  13. Intersect(l, n) → I
  14. OrthogonalLine(I, h) → p
  15. Intersect(p, h) → D
  16. If(3 < a < 4, Circle[I, (x(I) + ((a - 3) * (x(D) - x(I))), y(I) + ((a - 3) * (y(D) - y(I))))], a ≟ 4, Circle[I, D]) → c

AI Drawing Prompt Reference

Draw a triangle ABC, then construct the angle bisectors of angles A, B, and C, and find their intersection as the center of the incircle. Next, based on the distance from the center to the sides, draw the incircle. Specifically, first draw the three sides of the triangle, then construct the angle bisectors of angles A, B, and C, find their intersection as the center, and finally draw the incircle based on the distance from the center to the sides.
The prompt above was compiled from the original drawing commands and is for reference only.