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Circle Intersections by chritsopher

Circle Intersections by chritsopher
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2019-12-02 19:43
CircleCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the intersection conditions between circles, lines, and points, involving core math concepts like circle equations, coordinate geometry, quadratic equations, tangent lines, symmetry, incircle, reflection, definite integrals, and arithmetic mean. It is constructed using GeoGebra commands such as Line, Intersect, Ray, Point, Segment, Distance, and Circle, making it suitable for high school mathematics students and teachers for teaching and exploration purposes.

GeoGebra Commands & Parameters

  1. Line(A, C) → f
  2. Intersect(f, xAxis) → D
  3. Ray(D, A) → g
  4. Point(g) → E
  5. Segment(D, E) → h
  6. Line(G, F) → i
  7. Intersect(i, xAxis) → H
  8. Line(E, xAxis) → j
  9. Intersect(i, j) → I
  10. Ray(I, J) → k
  11. Point(k) → K
  12. Segment(H, K) → l
  13. Segment(L, M) → m
  14. Line(O, N) → n
  15. Intersect(n, xAxis) → P
  16. Segment(Q, P) → p
  17. Line(R, S) → q
  18. Intersect(q, xAxis) → T
  19. Distance(H, K) → a
  20. Line(K, xAxis) → r
  21. Intersect(q, r) → U
  22. Line(A_1, Z) → t
  23. Intersect(t, xAxis) → B_1
  24. Intersect(r, t) → C_1
  25. Line(E, U) → s
  26. Line(D, s) → b
  27. Intersect(q, b) → V
  28. Circle(U, V) → c
  29. Intersect(c, q, 2) → W
  30. Line(E, C_1) → f_1
  31. Line(D, f_1) → g_1
  32. Intersect(t, g_1) → D_1
  33. Circle(L, Segment[H, K]) → c_1
  34. Circle(M, h) → d_1
  35. Segment(D_1, B_1) → h_1
  36. Segment(W, T) → d
  37. Circle(L, h_1) → e
  38. Circle(L, d) → e_1