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Intersection's Locus

Intersection's Locus
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2014-05-11 00:01
CircleAngleCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the locus of intersection points. It involves core mathematical concepts such as circles and angles. Using GeoGebra commands like Intersect, Rotate, and Angle, the dynamic locus of intersection points can be constructed. Suitable for high school mathematics education and learning, particularly in coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(xAxis, yAxis) → P_2
  4. Intersect(p_3, q_3, (1, 0)) → B
  5. Rotate(B, π / n, P_2) → B'
  6. Angle(B, P_2, B') → α
  7. OrthogonalLine(B', xAxis) → b
  8. Intersect(c, b, 1) → C
  9. Polygon(C, B', n) → poly1, d, m, n_3, j_1, l_1, n_1, r_1, t_1, b_2, d_2, f_2, e, h_2, j_2, l_2, n_2, q_2, s_2, a_3, c_3, e_3, f_3, f, g_3, D, E, F, G, H, I, J, K, L, g, W, A_1, C_1, H_1, J_1, L_1, N_1, P_1, R_1, T_1, h, V_1, Z_1, B_2, D_2, F_2, H_2, J_2, K_2, L_2, i, j, k, l
  10. Circle(B, s) → p
  11. Intersect(p, xAxis, 1) → M
  12. Circle(M, s) → q
  13. Rotate(M, (π * (n - 2) / ((2 * n))), B) → M'
  14. Angle(M, B, M') → β
  15. Ray(B, M') → r
  16. Intersect(q, r, 2) → N
  17. Polygon(N, B, n) → poly2, t, i_1, k_1, m_1, p_1, q_1, s_1, a_2, c_2, e_2, g_2, a_1, i_2, k_2, m_2, p_2, r_2, t_2, b_3, d_3, h_3, i_3, b_1, j_3, O, P, Q, R, S, T, U, V, D_1, c_1, E_1, F_1, G_1, I_1, K_1, M_1, O_1, Q_1, S_1, U_1, d_1, W_1, A_2, C_2, E_2, G_2, I_2, M_2, N_2, O_2, e_1, f_1, g_1, h_1
  18. Intersect(d, a_1) → Z
  19. Intersect(d, t) → B_1