三角形特殊线段与外接圆动态演示
几何画板及绘图内容加载中,请稍等……
①本范例动态演示三角形内角平分线、中线、高线与外接圆的关系;②涉及核心概念:外接圆、三角形特殊线段、角度、几何变换;③构造要点:运用 Rotate, Ray, Point, Segment, Line, Intersect, Angle, Polygon, Circle, LineBisector, Min, Dilate, CircleSector, Vector, Translate 等命令构建图形;④适合高中及以上数学教学,用于理解几何性质与动态变化。
GeoGebra 命令及参数
Rotate(C, (a * π / 180), A) → A'Ray(A, A') → gPoint(g) → BSegment(B, C) → hSegment(A, B) → iPoint(i) → DSegment(A, C) → fLine(D, f) → jIntersect(j, h) → ESegment(E, C) → mLine(B, A) → kPoint(h) → FAngle(C, A, A') → αPolygon(A, C, B) → t1, c_1, b, a_1Polygon(D, E, F) → t2, f_1, d_1, eSegment(D, F) → lCircle(B, 2) → pCircle(A, 2) → qIntersect(p, k, 1) → HIntersect(q, k, 2) → IRay(B, H) → nRay(A, I) → rLineBisector(E, F) → sLineBisector(E, D) → tSegment(D, B) → g_1Segment(D, A) → h_1Min(g_1, h_1) → oCircle(A, (0.3 * o)) → e_1Circle(D, (0.3 * o)) → k_1Intersect(e_1, k) → K, LLineBisector(C, F) → j_1Dilate(D, If[0 < u ≤ 1, 1 - u, 0], E) → D'Segment(D, D') → l_1Rotate(K, If[1 < u ≤ 2, ((-(u - 1)) * α), (-α)], A) → K'CircleSector(A, K', K) → p_1Dilate(A, If[2 < u ≤ 3, 3 - u, 0], D) → B'Vector(A, B') → vTranslate(p_1, v) → q_1Dilate(D, If[4 < u ≤ 5, 5 - u, 0], F) → D'_1Segment(D, D'_1) → m_1Ray(D, A) → n_1LineBisector(E, F) → cLineBisector(F, D) → dLineBisector(F, C) → t_1LineBisector(D, E) → i_1LineBisector(F, D) → r_1Intersect(r_1, i_1) → G_1Circle(G_1, F) → s_1LineBisector(F, C) → f_2Intersect(s_1, k) → G, JLineBisector(J, A) → b_1LineBisector(C, F) → g_2Intersect(g_2, b_1) → MCircle(M, C) → c_2Ray(D, B) → h_2Intersect(s_1, h_2) → N, OLineBisector(O, A) → i_2LineBisector(C, F) → j_2Intersect(i_2, j_2) → PCircle(P, C) → d_2Dilate(G_1, If[6 < u ≤ 7, 7 - u, 0], F) → QSegment(G_1, Q) → k_2Circle(G_1, Q) → e_2Dilate(P, If[8.5 < u ≤ 9.5, 9.5 - u, 0], C) → P'Segment(P, P') → l_2Circle(P, P') → p_2Dilate(M, If[8.5 < u ≤ 9.5, 9.5 - u, 0], C) → M'Segment(M, M') → m_2Circle(M, M') → q_2
AI 绘图提示语参考
画一个三角形,并动态展示其角平分线、中线、高线与外接圆的关系。首先绘制三角形,然后找到各边的中点和高线交点,绘制角平分线、中线和高线。接着,以三角形的顶点为圆心绘制外接圆,并找到角平分线与外接圆的交点。最后,通过旋转和缩放操作,动态展示这些几何元素之间的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。