Inscribed and Circumscribed Polygon

Loading the math board and drawing, please wait…

2022-06-06 04:14

This example demonstrates the concepts of inscribed and circumscribed polygons. Key mathematical concepts include polygons, circles, and geometric construction. Using GeoGebra commands such as Circle, Point, Rotate, and Polygon, you can construct inscribed and circumscribed polygons. Suitable for middle and high school students learning about polygons and geometry.

GeoGebra Commands & Parameters

Circle(A, 1) → c
Point(c) → B
Rotate(B, (360 / a)°, A) → B'
Polygon(B, B', a) → poly1, f, k_1, m_1, p_1, r_1, t_1, b_1, d_1, f_2, h_2, j_2, g, l_2, n_2, q_2, s_2, a_2, c_2, e_2, f_3, g_3, h_3, h, m_3, p_3, r_3, t_3, a_3, b_3, c_3, h_4, i_4, j_4, q, k_4, l_4, m_4, n_4, c_4, d_4, e_4, f_5, g_5, m_5, s, n_5, C, G, I, K, M, O, Q, S, U, b, W, A_1, C_1, E_1, G_1, I_1, K_1, M_1, O_1, Q_1, e, S_1, U_1, W_1, A_2, C_2, D_2, E_2, F_2, K_2, M_2, g_1, O_2, Q_2, R_2, S_2, T_2, A_3, B_3, C_3, D_3, E_3, i_1, F_3, G_3, O_3, P_3, Q_3, R_3, S_3, A_4, B_4
OrthogonalLine(A, f) → i
OrthogonalLine(A, g) → j
Tangent(B, c) → k,
Intersect(i, k) → D
Tangent(B', c) → l,
Intersect(j, l) → E
Polygon(D, E, a) → poly2, m, l_1, n_1, q_1, s_1, a_1, c_1, e_1, g_2, i_2, k_2, n, m_2, p_2, r_2, t_2, b_2, d_2, i_3, j_3, k_3, l_3, p, n_3, q_3, s_3, d_3, e_3, f_4, g_4, p_4, q_4, r_4, r, s_4, t_4, a_4, b_4, h_5, i_5, j_5, k_5, l_5, p_5, t, q_5, F, H, J, L, N, P, R, T, V, d, Z, B_1, D_1, F_1, H_1, J_1, L_1, N_1, P_1, R_1, f_1, T_1, V_1, Z_1, B_2, G_2, H_2, I_2, J_2, L_2, N_2, h_1, P_2, U_2, V_2, W_2, Z_2, H_3, I_3, J_3, K_3, L_3, j_1, M_3, N_3, T_3, U_3, V_3, W_3, Z_3, C_4, D_4
Circle(A_{5}, 1) → c_{5}
Point(c_{5}) → B_{5}
Rotate(B_{5}, (360 / a)°, A_{5}) → B'_{1}
Polygon(B_{5}, B'_{1}, a) → poly1_{1}, f_{6}, k_{6}, m_{6}, p_{6}, r_{5}, t_{5}, b_{6}, d_{5}, f_{7}, h_{7}, j_{6}, g_{6}, l_{6}, n_{6}, q_{7}, s_{6}, a_{5}, c_{6}, e_{6}, f_{8}, g_{8}, h_{8}, h_{6}, m_{7}, p_{7}, r_{6}, t_{6}, a_{6}, b_{7}, c_{7}, h_{9}, i_{7}, j_{7}, q_{6}, k_{7}, l_{7}, m_{8}, n_{7}, c_{8}, d_{6}, e_{7}, f_{9}, g_{9}, m_{9}, s_{5}, n_{8}, C_{5}, G_{4}, I_{4}, K_{4}, M_{4}, O_{4}, Q_{4}, S_{4}, U_{4}, b_{5}, W_{4}, A_{6}, C_{6}, E_{4}, G_{5}, I_{5}, K_{5}, M_{5}, O_{5}, Q_{5}, e_{5}, S_{5}, U_{5}, W_{5}, A_{7}, C_{7}, D_{5}, E_{5}, F_{4}, K_{6}, M_{6}, g_{7}, O_{6}, Q_{6}, R_{4}, S_{6}, T_{4}, A_{8}, B_{6}, C_{8}, D_{6}, E_{6}, i_{6}, F_{5}, G_{6}, O_{7}, P_{4}, Q_{7}, R_{5}, S_{7}, A_{9}, B_{7}
Tangent(B_{5}, c_{5}) → k_{8},
Tangent(B'_{1}, c_{5}) → l_{8},

AI Drawing Prompt Reference

Draw a circle and choose a starting point on its circumference. Rotate this point about the circle’s center by equal steps (360 divided by an integer parameter) to generate the remaining points, then connect them to form an inscribed regular polygon. Next, at each relevant rotated point construct the tangent to the same circle, take intersections of the corresponding tangents to obtain new vertices, and connect these vertices to form the circumscribed polygon that relates to the inscribed one. Emphasize the tangent constructions at the circle points and the way their intersections define the outer polygon.

The prompt above was compiled from the original drawing commands and is for reference only.