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Congruent Incircles

Congruent Incircles
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2015-06-28 02:30
TriangleCircleGeometric Construction
This example demonstrates how to divide a given triangle into two smaller triangles with congruent incircles. Key concepts include triangles, incircles, and geometric construction. It uses Polygon, Angle, Intersect, Point, Incircle, Segment, Radius, etc., in GeoGebra. Suitable for high school geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(C, A, B) → α
  3. Intersect(f, g, (3.653557349755721, -2.34186191480298)) → E
  4. Point(Segment[A, C], x(E) / b) → D
  5. Incircle(A, B, D) → d
  6. Incircle(C, B, D) → e
  7. Segment(B, D) → h
  8. Radius(d) → i
  9. Radius(e) → j
  10. Point(Ray[F, F + (1, 0)]) → G

AI Drawing Prompt Reference

Draw a triangle ABC and then construct two smaller triangles within it that have congruent incircles. First, draw triangle ABC, then measure angle A, and find the midpoint D of side AC such that BD is perpendicular to AC. Next, construct two incircles with vertices A, B, D and C, B, D respectively, ensuring their radii are equal to prove that these two smaller triangles have the same incircle.
The prompt above was compiled from the original drawing commands and is for reference only.