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In-circle of triangle

In-circle of triangle
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2019-03-27 16:16
TriangleCircleGeometric Construction
This example demonstrates the construction of the incircle of a triangle and its geometric properties. Key mathematical concepts include circles, triangles, geometric construction, and locus. The construction involves GeoGebra commands such as Polygon, LineBisector, Intersect, and Circle, using objects like A, B, C, and others. It is suitable for middle or high school mathematics education to understand the relationship between triangles and circles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. LineBisector(C, B) → i
  3. LineBisector(A, B) → j
  4. Intersect(i, j) → D
  5. Intersect(i, g) → E
  6. Intersect(j, f) → F
  7. LineBisector(C, A) → k
  8. Intersect(k, h) → G
  9. Circle(D, E) → c
  10. Point(c) → H
  11. Segment(H, C) → l
  12. Segment(H, B) → m
  13. Segment(H, A) → n
  14. Point(c) → K
  15. Segment(D, K) → t
  16. Intersect(c, t, 1) → L

AI Drawing Prompt Reference

Draw a triangle and find the intersection point of its three angle bisectors, which is the incenter. Draw a circle with the incenter as the center and the radius equal to the distance from the incenter to one side of the triangle, making it tangent to all three sides. Then, draw segments from the incenter to each vertex, perpendicular to the corresponding sides.
The prompt above was compiled from the original drawing commands and is for reference only.