两圆外切圆心轨迹
几何画板及绘图内容加载中,请稍等……
该范例演示了两圆外切时圆心的轨迹。核心数学概念包括圆、几何、轨迹。使用了Intersect、Point、Circle、PointIn、Line、Midpoint、OrthogonalLine、Segment、Distance、Circumference等GeoGebra命令。适合初中及以上学生学习几何作图。
GeoGebra 命令及参数
Intersect(xAxis, yAxis) → APoint(yAxis) → OCircle(O, r_1) → cPointIn(b) → CCircle(C, r_2) → dLine(O, C) → hIntersect(c, h) → D, EIntersect(d, h) → F, GMidpoint(E, F) → ICircle(I, F) → kMidpoint(O, C) → M_3OrthogonalLine(M_3, h) → pCircle(O, r_1 + Δr) → qCircle(C, r_2 + Δr) → rIntersect(r, q) → L_2, L_1, ,Segment(O, L_1) → iSegment(O, L_2) → jSegment(L_1, C) → lSegment(L_2, C) → mIntersect(d, l) → L,Intersect(d, m) → N,Intersect(c, i) → P,Intersect(c, j) → Q,Circle(L_1, P) → sCircle(L_2, Q) → tMidpoint(D, G) → MCircle(O, R) → gCircle(C, R + r_1 - r_2) → c_1Intersect(g, c_1) → M_1, M_2, ,Line(M_1, O) → f_1Intersect(c, q, 1) → HIntersect(c, q, 1) → SIntersect(c, q) → T, , ,Intersect(c, f_1) → U, VLine(M_1, C) → g_1Intersect(d, r, 1) → WIntersect(d, r) → Z, , ,Intersect(d, r, 1) → A_1Intersect(d, r, 1) → B_1Intersect(d, r, 1) → C_1Intersect(d, r, 1) → D_1Intersect(d, r, 1) → E_1Intersect(d, r, 1) → F_1Intersect(d, g_1) → G_1, H_1Circle(M_1, V) → d_1Circle(C, r_2) → e_1Line(M_2, O) → aLine(M_2, C) → i_1Intersect(c, a) → B, I_1Intersect(d, r, 1) → J_1Intersect(d, r, 1) → K_1Intersect(d, r, 1) → L_3Circle(M_2, I_1) → k_1Distance(M_1, H_1) → distanceM1H1Distance(M_1, V) → distanceM1VCircumference(c) → circumferencecPointIn(c) → PointcIntersect(c_1, h, 1) → N_1Circle(M, G) → p_1
AI 绘图提示语参考
画两个外切的圆,找到它们的圆心轨迹。先画出坐标轴的交点,以其中一个圆心为圆心画圆,再以该圆上一点为圆心画另一个圆。连接两个圆心并找到交点,以交点为圆心画圆。接着,找到两个圆的中点,画出其中一点的垂线。再画出两个圆扩大后的交点,连接圆心与交点,并画出相关线段。最后,画出两个圆扩大后的交点与圆心的连线,并完成所有相关图形的绘制。
以上提示语为根据原始绘图命令整理而来,仅供参考。