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Inscribed and Circumscribed Polygons by Guillermo Bautista

Inscribed and Circumscribed Polygons by Guillermo Bautista
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2022-11-19 11:44
CirclePolygonGeometric Construction
This example demonstrates the relationship between polygons and their inscribed and circumscribed circles. It involves core mathematical concepts such as area, circle, limits, polygons, isosceles triangles, percentages, variance, addition, circumcircle or circumscribed circle. The construction uses GeoGebra commands like Point, Circle, Intersect, Rotate, Polygon, Tangent, and objects including A, c, n, B, C, C', poly1, f, g, h, i, j, k, l, m, p, q, r, s, t, a, b, d, e, f_1, g_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, D, E, F. It is suitable for high school students learning geometry to understand the geometric relationships and calculations involving polygons and circles.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → C
  4. Rotate(C, B, A) → C'
  5. Polygon(C, C', n) → poly1, f, q, r, s, t, a, b, d, e, f_1, g_1, g, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, h, s_1, D, E, F, G, H, I, J, K, L, i, M, N, O, P, Q, R, S, T, U, V, j, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, k, l, m, p
  6. Tangent(C, c) → t_1,
  7. Tangent(C', c) → a_1,
  8. Tangent(D, c) → b_1,
  9. Intersect(t_1, a_1) → H_1
  10. Intersect(a_1, b_1) → I_1
  11. Polygon(H_1, I_1, n) → poly2, c_1, l_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_2, b_2, d_1, c_2, d_2, e_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, e_1, m_3, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, f_2, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, g_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, h_2, i_2, j_2, k_2
  12. Circle(A, C) → c_3

AI Drawing Prompt Reference

Draw a figure consisting of a circle and triangles. The circle is centered at the origin with radius 1. The circle intersects the x-axis at points C and C'. Rotate C' around point B to C'. Connect C and C' to form a line segment, and construct a triangle poly1 around this segment. Draw tangents from C and C' to the circle, and find their intersection points H_1 and I_1. Then construct another triangle poly2 using H_1, I_1, and n points. Finally, draw circle c_3 with center A and point C. Ensure the figure shows the relationships between the circle, triangles, and tangents.
The prompt above was compiled from the original drawing commands and is for reference only.