MathPlotAI Logo MathPlotAI

Rectangle Triangle build upon c & a+b

Rectangle Triangle build upon c & a+b
Loading the math board and drawing, please wait…
2016-11-05 17:54
TrianglePolygonCoordinate GeometryLimitGeometric Construction
This example demonstrates how to construct a rectangle triangle based on side lengths c and a+b within a triangle. It involves core mathematical concepts like coordinate geometry, median line, orthocenter, quadratic equations, limits, and numbers. The construction uses commands and objects such as Point, Intersect, Line, Polygon, Circle, Tangent, Segment, OrthogonalLine in GeoGebra. Suitable for high school and above students to explore complex geometric relationships and constructions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B_1
  3. Intersect(xAxis, yAxis) → O
  4. Line(A_1, xAxis) → f
  5. Line(A_2, yAxis) → g
  6. Line(A, yAxis) → h
  7. Line(A_3, xAxis) → i
  8. Intersect(g, i) → E
  9. Intersect(f, g) → F
  10. Intersect(f, h) → G
  11. Intersect(h, i) → H
  12. Polygon(E, F, G, H) → poly1, e, f_1, g_1, h_1
  13. Point(xAxis) → B
  14. Circle(O, B_1) → c_1
  15. Point(c_1) → C
  16. Tangent(C, c_1) → j,
  17. Tangent(C_1, c_1) → k, a_1
  18. Intersect(j, k) → D
  19. Circle(O, D) → d
  20. Intersect(d, g_1, 2) → I
  21. Intersect(d, f_1, 2) → J
  22. Intersect(d, e, 2) → K
  23. Intersect(d, h_1, 2) → L
  24. Polygon(J, K, L, I) → poly2, j_1, k_1, l, i_1
  25. Segment(L, H) → a
  26. Segment(H, I) → b
  27. Segment(L, I) → c
  28. OrthogonalLine(L, h_1) → s
  29. OrthogonalLine(I, g_1) → t
  30. Intersect(s, t) → M
  31. Intersect(t, e) → N
  32. Intersect(e, h_1) → P
  33. Polygon(L, M, N, P) → poly3, l_1, m_1, n_1, p_1
  34. Intersect(s, f_1) → Q
  35. Intersect(t, g_1) → R
  36. Intersect(f_1, g_1) → S
  37. Polygon(Q, M, R, S) → poly4, q_1, m_2, r, s_1
  38. Segment(B_1, O) → r_1
  39. Segment(O, A) → t_1
  40. Polygon(L, R, H) → poly5, h_2, l_2, r_2

AI Drawing Prompt Reference

Construct a coordinate system with x and y axes. Mark two points on the x-axis and draw perpendicular lines from these points to the y-axis and vice versa, forming a quadrilateral. Draw a circle centered at the origin with a radius equal to the distance from the origin to one point on the x-axis. From a point on this circle, draw tangents to the circle, and find their intersection. Use this intersection point to draw another circle, intersecting the sides of the quadrilateral. Connect various intersection points to form multiple triangles and quadrilaterals, highlighting complex geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.