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In-circle of Square by Timur Kapitsa

In-circle of Square by Timur Kapitsa
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2019-03-29 02:05
CircleGeometric Construction
This example demonstrates the in-circle of a square. Key mathematical concepts include geometric transformations and properties of circles. Using GeoGebra commands such as Polygon, LineBisector, Intersect, Segment, Circle, and Point, the in-circle of a square can be constructed. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. LineBisector(D, A) → j
  3. LineBisector(D, C) → k
  4. Intersect(k, h) → F
  5. Intersect(j, g) → G
  6. Intersect(k, f) → H
  7. Intersect(j, i) → I
  8. Segment(F, H) → l
  9. Segment(I, G) → m
  10. Intersect(l, m) → E
  11. Circle(E, G) → c
  12. Segment(E, C) → n
  13. Segment(E, B) → p
  14. Segment(E, A) → q
  15. Segment(E, D) → r
  16. Intersect(c, r, 1) → J
  17. Intersect(c, n, 1) → K
  18. Intersect(c, p, 1) → L
  19. Intersect(c, q, 1) → M
  20. Polygon(J, K, L, M) → q1, j_1, k_1, l_1, m_1
  21. Intersect(m, m_1) → N
  22. Intersect(l, j_1) → O
  23. Intersect(m, k_1) → P
  24. Intersect(l, l_1) → Q
  25. Circle(E, P) → d
  26. Point(d) → R
  27. Segment(R, D) → s
  28. Segment(R, A) → a
  29. Segment(R, B) → b
  30. Segment(R, C) → e
  31. Point(d) → S
  32. Segment(E, S) → t

AI Drawing Prompt Reference

Start with a square. Construct the perpendicular bisectors of two opposite sides, which intersect the square's sides at four points. Connect these points to form two crossing segments; their intersection is the square's center. Draw a circle centered at this point with radius to a vertex, which is tangent to all sides (the incircle). Then draw another circle centered at the same point with radius to the intersection of the crossing segments and the incircle. Finally, pick a point on this second circle, connect it to the four vertices and to the center, creating several segments.
The prompt above was compiled from the original drawing commands and is for reference only.