内切圆扩展 - GoGeometry 动态演示
几何画板及绘图内容加载中,请稍等……
这是一个动态可修改的几何问题演示,由 Antonio Gutierrez 提出。该范例展示了内切圆的扩展,涉及三角形和圆的相关概念。通过旋转、角度、线段等 GeoGebra 命令,可以构造出动态的几何图形。适合初中及以上学生和教师使用,帮助理解几何作图和内切圆的相关性质。
GeoGebra 命令及参数
Rotate(A, (a * π / 180), B) → A'Angle(A, B, A') → αSegment(B, A) → fRay(B, A') → gPoint(g) → CSegment(A, C) → hSegment(B, C) → iPolygon(B, A, C) → t1, c, b, a_1Angle(C, A, B) → βAngle(B, C, A) → γRotate(C, β / 2, A) → C'Angle(C, A, C') → δRotate(A, α / 2, B) → A'_1Angle(A, B, A'_1) → εRotate(B, γ / 2, C) → B'Angle(B, C, B') → ζRay(B, A'_1) → jRay(A, C') → kRay(C, B') → lIntersect(j, k) → DMin({i, f, h}) → dCircle(B, (0.2 * d)) → eCircle(A, (0.2 * d)) → pCircle(C, (0.2 * d)) → qOrthogonalLine(D, f) → mOrthogonalLine(D, h) → nOrthogonalLine(D, i) → rIntersect(m, f) → EIntersect(n, h) → FIntersect(r, i) → GIntersect(e, j, 1) → HIntersect(p, k, 1) → IIntersect(p, h, 1) → JIntersect(e, f, 1) → KIntersect(q, i) → L,Intersect(q, l, 1) → MRotate(K, If[1 < o ≤ 2, ((o - 1) * ε), ε], B) → K'Dilate(B, If[0 < o ≤ 1, 1 - o, 0], D) → B'_1Segment(B, B'_1) → sCircleSector(B, K, K') → tRotate(t, If[3 < o ≤ 4, ((o - 3) * ε), ε], B) → t'Dilate(A, If[4 < o ≤ 5, 5 - o, 0], D) → A'_2Segment(A, A'_2) → f_1Rotate(J, If[5 < o ≤ 6, ((o - 5) * δ), δ], A) → J'CircleSector(A, J, J') → c_1Rotate(c_1, If[7 < o ≤ 8, ((o - 7) * δ), δ], A) → d_1Dilate(C, If[8 < o ≤ 9, 9 - o, 0], D) → C'_1Segment(C, C'_1) → h_1Rotate(L, If[9 < o ≤ 10, ((o - 9) * ζ), ζ], C) → L'CircleSector(C, L, L') → e_1Rotate(e_1, If[11 < o ≤ 12, ((o - 11) * ζ), ζ], C) → k_1Dilate(D, If[13 < o ≤ 14, 14 - o, 0], E) → D'Dilate(D, If[14 < o ≤ 15, 15 - o, 0], F) → D'_1Dilate(D, If[15 < o ≤ 16, 16 - o, 0], G) → D'_2Segment(D, D') → i_1Segment(D, D'_1) → j_1Segment(D, D'_2) → l_1Angle(D, E, B) → ηAngle(D, F, A) → θAngle(D, G, C) → ιAngle(E, D, F) → κAngle(F, D, G) → λRotate(D, If[17 < o ≤ 18, ((o - 17) * κ), κ], D) → D'_3Rotate(D', If[17 < o ≤ 18, ((o - 17) * κ), κ], D) → D''Segment(D'_3, D'') → m_1Rotate(D'_3, If[18 < o ≤ 19, ((o - 18) * λ), λ], D) → PRotate(D'', If[18 < o ≤ 19, ((o - 18) * λ), λ], D) → D'''Segment(P, D''') → n_1Rotate(G, If[19 < o ≤ 21, ((o - 19) * π), (2 * π)], D) → G'CircleArc(D, G, G') → p_1Circle(D, E) → q_1Line(G, F) → g_1Line(B, D) → r_1Intersect(g_1, r_1) → NLine(N, A) → s_1Circle(N, (0.1 * d)) → t_1Intersect(t_1, s_1) → O, QIntersect(t_1, r_1) → R, SCircle(G, 1) → c_2Circle(F, 1) → d_2Intersect(c_2, g_1) → T, UIntersect(d_2, g_1) → V, WRay(F, W) → f_2Dilate(G, If[22 < o ≤ 23, 23 - o, 0], F) → G'_1Segment(G, G'_1) → g_2Dilate(D, If[24 < o ≤ 25, 25 - o, 0], N) → A'_3Segment(D, A'_3) → h_2Ray(N, O) → i_2Dilate(A, If[25 < o ≤ 26, 26 - o, 0], N) → A'_4Segment(A, A'_4) → j_2Rotate(O, If[27 < o ≤ 28, ((o - 27) * π / 2), π / 2], N) → O'CircleSector(N, O, O') → e_2Rotate(e_2, If[29 < o ≤ 30, ((o - 29) * π / 2), π / 2], N) → k_2
AI 绘图提示语参考
绘制一个三角形ABC,然后构造其内切圆,并通过旋转和缩放等操作,生成一系列与内切圆相关的点和线段,最终形成一个包含多个圆和线段的复杂图形。首先画出三角形ABC,接着构造内切圆,然后通过旋转和缩放生成新的点和线段,最后连接这些点和线段形成最终的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。