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Inscribe and Circumscribe Regular Polygon

Inscribe and Circumscribe Regular Polygon
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2019-07-11 19:48
CirclePolygonGeometric Construction
In collections Calculating areas as an approach to the notions of limit and
This example demonstrates how to inscribe and circumscribe regular polygons using GeoGebra. It involves core mathematical concepts such as circles, polygons, geometric constructions, and rotations. Key GeoGebra commands and objects used include Circle, Point, Line, Segment, Rotate, and Polygon. Suitable for high school mathematics teaching or for geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Circle(C, r) → c
  2. Point(c) → A
  3. Textfield(r) → CasillaDeEntrada2
  4. Line(C, A) → l
  5. IterationList(x + 1, 0, 200) → l1
  6. Segment(A, C) → RADIUS
  7. Point(c) → D
  8. Rotate(D, a°, C) → D'
  9. Polygon(D, D', n) → polígono1, f, s, t, b, d, e, f_1, g_1, h_1, i_1, j_1, g, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, a_1, h, b_1, c_1, d_1, E, F, G, H, I, J, K, i, L, M, N, O, P, Q, R, S, T, U, j, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, k, H_1, I_1, J_1, m, p, q
  10. LineBisector(f) → e_1
  11. Intersect(c, e_1) → K_1, L_1
  12. OrthogonalLine(K_1, e_1) → f_2
  13. Line(D, C) → g_2
  14. Line(C, D') → h_2
  15. Intersect(f_2, g_2) → M_1
  16. Intersect(f_2, h_2) → N_1
  17. Polygon(M_1, N_1, n) → polígono2, i_2, s_2, t_2, a_2, b_2, c_2, d_2, e_2, f_3, g_3, h_3, j_2, i_3, j_3, k_3, l_3, m_3, n_3, p_3, q_3, r_3, s_3, k_2, t_3, a_3, b_3, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, l_2, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, m_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, n_2, R_2, S_2, T_2, p_2, q_2, r_2

AI Drawing Prompt Reference

Draw a circle and mark its center and radius. Create a point on the circle and draw a line from the center to this point. Rotate this line around the center multiple times to form several points. Use these points to draw a regular polygon. Then, find the perpendicular bisector of the line and locate its intersections with the circle. Using these intersections, draw another regular polygon that is tangent to the first one. Finally, display both polygons, one inscribed within the circle and the other circumscribed around it, clearly showing the relationship between inscribed and circumscribed regular polygons.
The prompt above was compiled from the original drawing commands and is for reference only.