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Presentation of Equiangular Octagon Construction with Circumscribed Circle

Presentation of Equiangular Octagon Construction with Circumscribed Circle
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2017-02-10 04:04
CirclePolygonAngleGeometric Construction
This example demonstrates constructing an equiangular octagon with a circumscribed circle that is not regular. It involves core geometry concepts like circles, polygons, angles, tangents, and reflections. The construction utilizes GeoGebra commands including Circle, Point, Polygon, Angle, Line, Intersect, Tangent, and Mirror. Suitable for high school geometry students or math enthusiasts exploring properties of equiangular polygons versus regular polygons.

GeoGebra Commands & Parameters

  1. Circle(B, C) → c
  2. Point(c, 0) → D
  3. Point(c, 0.25) → E
  4. Point(c, 0.5) → F
  5. Point(c, 0.75) → G
  6. Point(c, a) → H
  7. Point(c, a + 0.25) → I
  8. Point(c, a + 0.5) → J
  9. Point(c, a + 0.75) → K
  10. Polygon(D, H, E, I, F, J, G, K) → poly1, d, h, e, i, f, j, g, k
  11. Angle(poly1) → α, β, γ, δ, ε, ζ, η, θ
  12. Polygon(D, G, F, E) → poly2, d_1, g_1, f_1, e_1
  13. Polygon(H, K, J, I) → poly3, h_1, k_1, j_1, i_1
  14. Line(D, H) → l
  15. Line(K, G) → m
  16. Line(J, F) → n
  17. Line(E, I) → p
  18. Intersect(l, m) → L
  19. Intersect(m, n) → M
  20. Intersect(n, p) → N
  21. Intersect(l, p) → O
  22. Polygon(O, L, M, N) → poly4, o, l_1, m_1, n_1
  23. Tangent(G, c) → q,
  24. Tangent(D, c) → r,
  25. Intersect(q, r) → P
  26. Mirror(P, G) → P'
  27. Mirror(P', F) → P''
  28. Mirror(P'', E) → P'''
  29. Polygon(P, P', P'', P''') → poly5, p_1, p', p'', p'''