直角三角形的垂心与勾股定理

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Circle(A, B, C) → d
3. Center(d) → O
4. OrthogonalLine(A, a) → f
5. OrthogonalLine(B, b) → g
6. OrthogonalLine(C, c) → h
7. Intersect(f, g) → H
8. Segment(H, B) → i
9. Mirror(B, O) → D
10. Segment(B, D) → j
11. If(0 < n ≤ 1, Segment[Translate[H, Dilate[H, 1 - n, C] - H], Translate[B, Dilate[H, 1 - n, C] - H]], If[n > 1, Segment[Translate[H, C - H], Translate[B, C - H]]]) → k
12. If(0 < n ≤ 1, Translate[B, Dilate[H, 1 - n, C] - H], If[n > 1, Translate[B, C - H]]) → B'
13. Angle(A, C, B') → α
14. Angle(B, O, B') → β
15. If(2 < n ≤ 3, Segment[Rotate[B, ((n - 2) * β), O], Rotate[D, ((n - 2) * β), O]], If[n > 3, Segment[A, B']]) → l