Kariya点与Feuerbach双曲线的几何可视化

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. TriangleCenter(A, B, C, 1) → I
3. ClosestPoint(a, I) → A_1
4. Circle(I, A_1) → d
5. Intersect(d, b, 1) → B_1
6. Intersect(d, c, 1) → C_1
7. Line(I, A_1) → f
8. Line(I, B_1) → g
9. Line(I, C_1) → h
10. Point(f, u) → X
11. Circle(I, X) → e
12. Line(A, X) → i
13. Intersect(e, h) → J, L
14. If((AffineRatio[I, C_1, L] * AffineRatio[I, A_1, X]) > 0, L, J) → Z
15. Line(C, Z) → k
16. Intersect(i, k) → K
17. Locus(K, X) → hF_{1}
18. AffineRatio(I, A_1, X) → l
19. AffineRatio(I, C_1, Z) → n
20. Intersect(e, g) → G, H_{1}
21. If((AffineRatio[I, B_1, G] * AffineRatio[I, A_1, X]) > 0, G, H_{1}) → Y
22. Midpoint(a) → M
23. Midpoint(b) → N
24. Midpoint(c) → O
25. Circle(M, N, O) → p
26. Intersect(p, d) → F, D, ,
27. Mirror(K, F) → K'
28. Segment(K, F) → j
29. Line(B, Y) → m
30. Segment(I, X) → q
31. Segment(I, Y) → r
32. Segment(I, Z) → s
33. TriangleCenter(A, B, C, 4) → H
34. TriangleCenter(A, B, C, 8) → Na
35. TriangleCenter(A, B, C, 7) → Ge
36. Radius(d) → o
37. TriangleCenter(A, B, C, 21) → Sc
38. Radius(e) → t
39. Conic(A, B, C, H, I) → hF