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Largest Possibility?

Largest Possibility?
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2021-12-16 01:09
TriangleCircleProbability & StatisticsOptimizationGeometric Construction
In collections Open Middle: Distance in the Coordinate Plane (2)
This example demonstrates the dynamic relationship between circumcircles and inscribed polygons of a triangle as its vertices are adjusted. Core math concepts include Natural Numbers, Quadratic Equations, Circumcircle, Congruence, and Stochastic Processes. Construction highlights involve commands like PointIn, Segment, SurdText, Textfield, Point, If, Mode, Intersect, Polygon, and Angle from GeoGebra. Suitable for high school and above, exploring geometric transformations and probability statistics connections.

GeoGebra Commands & Parameters

  1. PointIn(e) → A
  2. PointIn(e) → B
  3. Segment(A, B) → f
  4. SurdText(f) → text1
  5. Textfield(j) → InputBox1
  6. Textfield(k) → InputBox2
  7. Point(Circle[A, sqrt((100 * j) + (10 * k) + o)]) → C
  8. Segment(A, C) → l
  9. If(m < i, "Too short!", m > i, "Too long!", "This value is correct!") → text7
  10. Mode(l1) → l2
  11. Intersect(eq1, p) → D
  12. Polygon(A, D, B) → t1, b_1, a_1, d_1
  13. Segment(A, D) → q
  14. Segment(D, B) → r
  15. Angle(B, D, A) → α
  16. Textfield(o) → InputBox3
  17. If(Length[l2] ≟ 0, "All digits are different!", "Some digits repeat.") → text8

AI Drawing Prompt Reference

Place two vertices A and B in the plane and draw the segment AB. Construct the relevant circumcircle associated with this setup, then choose the third point C on that circle according to two adjustable input parameters (via a square-root expression). Connect A to C to complete the triangle framework, and determine a point D using the intersection of the circle with an additional condition curve so that D is tied to A and B. Draw the polygon A–D–B and label the angle at D, specifically ∠BDA (equivalently ∠B D A). Include text elements that reflect the chosen parameter range (e.g., indicating “too short,” “too long,” or “correct”) and another message depending on whether the digits satisfy a “all different / some repeat” condition.
The prompt above was compiled from the original drawing commands and is for reference only.