Radius in Right Triangles

Radius in Right Triangles
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2017-02-12 16:58
This example demonstrates the radius in right triangles. It involves basic concepts of right triangles and circles. Using GeoGebra commands such as Segment, Intersect, OrthogonalLine, Circle, etc., the construction of the radius in right triangles is illustrated. Suitable for middle and high school students learning geometric construction.

GeoGebra Commands & Parameters

  1. Segment(C, D) → f
  2. Segment(D, E) → g
  3. Segment(E, F) → h
  4. Segment(F, C) → i
  5. Segment(D, F) → j
  6. Segment(D, F) → k
  7. Segment(C, E) → l
  8. Intersect(k, l) → G
  9. OrthogonalLine(G, g) → m
  10. Intersect(m, g) → H
  11. Intersect(m, i) → I
  12. Circle(G, 1.5) → c
  13. Intersect(c, f, 1) → J
  14. Intersect(c, h, 1) → K
  15. Vector(G, I) → u
  16. Vector(G, J) → v
  17. Vector(G, H) → w
  18. Vector(G, K) → d
  19. Intersect(c, l, 1) → L
  20. Intersect(c, k, 1) → M
  21. Intersect(c, l, 2) → N
  22. Intersect(c, k, 2) → O
  23. Vector(G, M) → e
  24. Vector(G, L) → n
  25. Vector(G, N) → p
  26. Vector(G, O) → q
  27. OrthogonalLine(M, v) → r
  28. OrthogonalLine(M, xAxis) → s
  29. OrthogonalLine(N, d) → t
  30. OrthogonalLine(O, u) → f_1
  31. Point(u) → P
  32. Polygon(L, P, G) → poly1, g_1, l_1, p_1
  33. Point(v) → Q
  34. Polygon(L, Q, G) → poly2, g_2, l_2, q_1
  35. Polygon(Q, M, G) → poly3, g_3, q_2, m_1
  36. Point(w) → R
  37. Polygon(M, R, G) → poly4, g_4, m_2, r_1
  38. Polygon(R, N, G) → poly5, g_5, r_2, n_1
  39. Point(d) → S
  40. Polygon(N, S, G) → poly6, g_6, n_2, s_1
  41. Polygon(G, S, O) → poly7, o, g_7, s_2
  42. Polygon(G, P, O) → poly8, o_1, g_8, p_2
  43. Intersect(f_1, h) → T
  44. Polygon(O, T, F) → poly9, f_2, o_2, t_1
  45. Intersect(t, i) → U
  46. Polygon(O, U, F) → poly10, f_3, o_3, u_1
  47. Intersect(r, i) → V
  48. Polygon(C, L, V) → poly11, v_1, c_1, l_3
  49. Intersect(f_1, f) → W
  50. Polygon(W, L, C) → poly12, c_2, w_1, l_4
  51. Intersect(s, f) → Z
  52. Polygon(Z, M, D) → poly13, d_1, z_1, m_3
  53. Intersect(r, g) → A_1
  54. Polygon(D, A_1, M) → poly14, m_4, d_2, a_1
  55. Intersect(t, g) → B_1
  56. Polygon(N, B_1, E) → poly15, e_1, n_3, b_1
  57. Intersect(s, h) → C_1
  58. Polygon(N, E, C_1) → poly16, c_3, n_4, e_2

AI Drawing Prompt Reference

Draw a right triangle with its hypotenuse and two legs marked. Then, draw a circle centered at the right-angled vertex that is tangent to the hypotenuse, marking the points of tangency. Next, draw vectors from the center of the circle to the three vertices of the triangle and to the points of tangency. Finally, connect the intersection points of the circle with the triangle's boundaries to form several small polygons, illustrating the relationship between the circle and the right triangle.
The prompt above was compiled from the original drawing commands and is for reference only.