同圆心的内切圆
几何画板及绘图内容加载中,请稍等……
当另一个圆与任意三角形的内切圆具有相同的圆心时,会发生什么?通过互动工作表探索这一现象。本范例涉及三角形的内切圆及其性质。使用GeoGebra命令如Line, Rotate, Angle, Circle等进行几何作图。适合初中及以上学生学习三角函数和几何作图。
GeoGebra 命令及参数
Line(A, B) → fRotate(B, (a * π / 180), A) → B'Angle(B, A, B') → αRay(A, B') → gPoint(g) → CSegment(B, C) → hLine(A, C) → iLine(C, B) → jSegment(A, B) → kSegment(A, C) → lMin({h, k, l}) → bAngle(C, B, A) → βRotate(B, α / 2, A) → B'_1Angle(B, A, B'_1) → γRotate(C, β / 2, B) → C'Angle(C, B, C') → δRay(A, B'_1) → mRay(B, C') → nIntersect(m, n) → DSegment(D, C) → pSegment(D, A) → qSegment(D, B) → rMax({p, q, r}) → cCircle(D, d) → eIntersect(e, j, 1) → EIntersect(e, i, 2) → FIntersect(e, j, 2) → GIntersect(e, f) → H, IIntersect(e, i, 1) → JSegment(A, D) → sSegment(B, D) → tMin({s, t}) → oSegment(A, B) → f_1Circle(A, (0.35 * o)) → c_1Circle(B, (0.35 * o)) → d_1Intersect(c_1, f_1, 1) → KIntersect(c_1, s, 1) → LIntersect(d_1, h) → M,Intersect(d_1, t, 1) → NPolygon(H, A, J) → poly1, j_1, h_1, a_1Polygon(B, I, G) → poly2, g_1, b_1, i_1Polygon(C, F, E) → poly3, e_1, c_2, f_2Polygon(A, B, C) → poly4, c_3, a_2, b_2Angle(A, C, B) → εCircleSector(B, M, N) → k_1CircleSector(A, K, L) → p_1Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'Dilate(B, If[1 < u ≤ 2, 2 - u, 0], D) → B'_2Segment(B, B'_2) → l_1Segment(A, A') → m_1Rotate(p_1, If[2 < u ≤ 3, ((u - 2) * γ), γ], A) → q_1Rotate(k_1, If[3 < u ≤ 4, ((u - 3) * δ), δ], B) → r_1Dilate(D, If[4 < u ≤ 5, 5 - u, 0], F) → D'Circle(D, D') → s_1Segment(D, D') → n_1Dilate(C, If[5 < u ≤ 6, 6 - u, 0], F) → C'_1Dilate(C, If[5 < u ≤ 6, 6 - u, 0], E) → C'_2Dilate(A, If[5 < u ≤ 6, 6 - u, 0], H) → A'_1Dilate(A, If[5 < u ≤ 6, 6 - u, 0], J) → A'_2Dilate(B, If[5 < u ≤ 6, 6 - u, 0], I) → B'_3Dilate(B, If[5 < u ≤ 6, 6 - u, 0], G) → B'_4Segment(C, C'_1) → t_1Segment(C, C'_2) → g_2Segment(A, A'_1) → h_2Segment(A, A'_2) → i_2Segment(B, B'_3) → j_2Segment(B, B'_4) → k_2Dilate(F, If[6 < u ≤ 7, 7 - u, 0], E) → F'Dilate(H, If[6 < u ≤ 7, 7 - u, 0], J) → H'Dilate(G, If[6 < u ≤ 7, 7 - u, 0], I) → G'Segment(F, F') → l_2Segment(H, H') → m_2Segment(G, G') → n_2Rotate(C, If[7 < u ≤ 8, ((u - 7) * ε), ε], C) → C'_3Rotate(C'_1, If[7 < u ≤ 8, ((u - 7) * ε), ε], C) → OSegment(C'_3, O) → p_2Rotate(A, If[8 < u ≤ 9, ((u - 8) * α), α], A) → A'_3Rotate(A'_1, If[8 < u ≤ 9, ((u - 8) * α), α], A) → PSegment(A'_3, P) → q_2Rotate(B, If[9 < u ≤ 10, ((u - 9) * β), β], B) → B'_5Rotate(B'_4, If[9 < u ≤ 10, ((u - 9) * β), β], B) → QSegment(B'_5, Q) → r_2
AI 绘图提示语参考
绘制一个三角形ABC,然后以三角形ABC的内心为中心画一个圆。接着,通过旋转和角度计算,构造出与内心圆同心的另一个圆,并找到该圆与三角形边的交点,形成新的三角形DEF。最后,通过缩放操作,调整三角形ABC的顶点位置,观察变化。
以上提示语为根据原始绘图命令整理而来,仅供参考。