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Incircle and Excircle of a Regular Polygon

Incircle and Excircle of a Regular Polygon
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2019-11-12 04:12
CirclePolygonGeometric Construction
This GeoGebra example demonstrates the construction of incircles and excircles for regular polygons. It explores core mathematical concepts such as regular polygon properties, circle tangency, and the relationship between inscribed and circumscribed circles. The construction utilizes GeoGebra commands including Polygon, Circle, Center, Segment, OrthogonalLine, and Intersect, along with numerous labeled points for geometric positioning and calculation. It is suitable for high school geometry education, helping students visualize and understand polygon-circle interactions and dynamic geometric properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, n) → poly1, f, q, r, s, t, a, b, c, d, e, f_1, g, g_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1, q_1, h, r_1, s_1, t_1, a_1, C, D, E, F, G, H, i, I, J, K, L, M, N, O, P, Q, R, j, S, T, U, V, W, Z, A_1, B_1, C_1, D_1, k, E_1, F_1, G_1, H_1, I_1, l, m, p
  2. Circle(A, C, B) → c_1
  3. Center(c_1) → J_1
  4. Segment(J_1, A) → b_1
  5. Segment(J_1, B) → d_1
  6. Segment(J_1, C) → e_1
  7. Segment(J_1, D) → f_2
  8. Segment(J_1, E) → g_2
  9. Segment(J_1, F) → h_2
  10. Segment(J_1, G) → i_2
  11. Segment(J_1, H) → j_2
  12. Segment(J_1, I) → k_2
  13. Segment(J_1, J) → l_2
  14. Segment(K, J_1) → m_2
  15. Segment(L, J_1) → n_2
  16. Segment(J_1, M) → p_2
  17. Segment(N, J_1) → q_2
  18. Segment(J_1, O) → r_2
  19. Segment(P, J_1) → s_2
  20. Segment(J_1, Q) → t_2
  21. Segment(R, J_1) → a_2
  22. OrthogonalLine(J_1, f) → b_2
  23. Intersect(b_2, f) → K_1
  24. Circle(J_1, K_1) → c_2
  25. Segment(A, C) → d_2
  26. Segment(A, D) → e_2
  27. Segment(A, C) → f_3