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Studies on Incircles by Timur Kapitsa

Studies on Incircles by Timur Kapitsa
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2017-04-10 23:36
CirclePolygonGeometric Construction
This example demonstrates properties related to incircles. It mainly involves the properties of polygons and circles, and how to construct incircles using geometric construction tools. Commands used include polygon, midpoint, segment, intersect, and circle. Suitable for middle and high school students to learn about polygons and circles.

GeoGebra Commands & Parameters

  1. Polygon(C, D, 6) → poly1, a, I, b, d, e, f, g, E, G, H
  2. Midpoint(I, H) → B
  3. Midpoint(I, C) → F
  4. Midpoint(C, D) → J
  5. Midpoint(D, E) → K
  6. Midpoint(E, G) → L
  7. Midpoint(G, H) → M
  8. Segment(B, K) → c
  9. Segment(F, L) → h
  10. Segment(M, J) → i
  11. Intersect(c, h) → N
  12. Circle(N, L) → k
  13. Point(k) → A
  14. Segment(A, G) → j
  15. Segment(A, H) → l
  16. Segment(A, I) → m
  17. Segment(A, C) → n
  18. Segment(A, D) → p
  19. Segment(A, E) → q
  20. Segment(N, J) → R
  21. Segment(O, P) → s

AI Drawing Prompt Reference

Draw a regular hexagon with vertices arranged counterclockwise. Inside the hexagon, connect the midpoints of three pairs of opposite sides to form three segments that intersect at a common point. Using this intersection as the center, draw a circle passing through the midpoint of one side of the hexagon. Choose an arbitrary point on this circle, and from it draw segments to all six vertices of the hexagon. Finally, draw a segment from the circle's center to the midpoint of one side, and another segment connecting two unspecified points. The figure illustrates the relationships among the hexagon, its incircle, and various internal lines.
The prompt above was compiled from the original drawing commands and is for reference only.