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Angle between Chord and Tangent

Angle between Chord and Tangent
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2014-10-15 16:24
CircleAngleGeometric Construction
In collections Circle Geometry
This example illustrates the angle between a chord and a tangent, which is equal to the angle in the opposite segment according to the circle geometry theorem. Key concepts include the circle geometry theorem and properties of tangents. It uses commands like Polygon, Angle, Circle, Point, Segment, and Tangent in GeoGebra. Suitable for middle school and above students learning geometry.

GeoGebra Commands & Parameters

  1. Polygon(E_1, H_1, G_1, F_1) → poly1, e_2, h_2, g_2, f_2
  2. Angle(G_1, F_1, E_1) → λ
  3. Angle(E_1, H_1, G_1) → ξ
  4. Angle(F_1, E_1, H_1) → ο
  5. Angle(H_1, G_1, F_1) → ρ
  6. Circle(J_2, K_2) → r_2
  7. Point(r_2) → L_2
  8. Point(r_2) → M_2
  9. Segment(L_2, M_2) → s_2
  10. Segment(K_2, L_2) → t_2
  11. Segment(K_2, M_2) → i_3
  12. Tangent(K_2, r_2) → j_3,
  13. Point(j_3) → N_2
  14. Point(j_3) → T_2
  15. Segment(N_2, T_2) → k_3
  16. Angle(M_2, K_2, T_2) → τ_1
  17. Angle(M_2, L_2, K_2) → υ_1
  18. Angle(L_2, K_2, N_2) → ϕ_1
  19. Angle(L_2, M_2, K_2) → χ_1

AI Drawing Prompt Reference

Draw a circle and mark four points E, F, G, and H on it. Connect these points to form a quadrilateral. Draw the chord EF and EG, and the tangent at point H. Label the angle between the chord EF and the tangent, and the angle between the chord EG and the tangent.
The prompt above was compiled from the original drawing commands and is for reference only.