阿基米德双圆
几何画板及绘图内容加载中,请稍等……
这个范例展示了阿基米德证明的双圆定理,即紫色圆与外圆、红色圆及垂直分割线相切且全等。核心概念包括圆的性质、几何作图和相似性。使用了Midpoint、Circle、Point、OrthogonalLine等GeoGebra命令。适合高中几何学习。
GeoGebra 命令及参数
Midpoint(A, B) → CSegment(C, A) → gCircle(C, B) → cSegment(A, B) → aPoint(g) → DMidpoint(D, A) → GMidpoint(D, B) → HCircle(G, D) → dCircle(H, D) → eOrthogonalLine(D, a) → bIntersect(c, b, 2) → EIntersect(c, b, 1) → FSegment(E, F) → fDistance(G, A) → rDistance(H, B) → RSegment(I, G) → jOrthogonalLine(I, f) → kIntersect(b, k) → JSegment(I, J) → lIntersect(d, j) → K,Segment(I, K) → mCircle(D, G) → pIntersect(p, a, 2) → LOrthogonalLine(L, a) → iParabola(G, i) → qCircle(D, H) → sLine(A, B) → nIntersect(s, n, 1) → MOrthogonalLine(M, n) → tParabola(H, t) → c_1Ray(C, I) → a_1Intersect(c, a_1, 1) → NSegment(I, N) → b_1Circle(G, C) → d_1Intersect(d_1, n, 1) → OOrthogonalLine(O, n) → e_1Parabola(C, e_1) → f_1Circle(H, C) → g_1Intersect(g_1, n, 2) → POrthogonalLine(P, n) → h_1Parabola(C, h_1) → k_1Intersect(c_1, k_1, 2) → QIntersect(c_1, k_1, 1) → SIntersect(q, f_1, 1) → TIntersect(q, f_1, 2) → UOrthogonalLine(Q, f) → i_1OrthogonalLine(S, f) → j_1OrthogonalLine(U, f) → l_1OrthogonalLine(T, f) → m_1Intersect(i_1, f) → VIntersect(m_1, f) → WIntersect(l_1, f) → ZIntersect(j_1, f) → A_1Circle(Q, V) → p_1Circle(T, W) → q_1Circle(U, Z) → r_1Circle(S, A_1) → s_1Area(p_1) → oPointIn(p_1) → Pointp1Area(q_1) → uPointIn(q_1) → Pointq1
AI 绘图提示语参考
画一个包含外圆和内切紫圆的几何图形,紫圆同时切于外圆和垂直分割线,并展示其与外圆和分割线的全等关系。先画出外圆和垂直分割线,再找到外圆与分割线的交点,以此点为圆心画内切紫圆。接着,通过几何方法构建两个辅助圆,并利用这些圆和线段找到关键点,最终形成完整的图形,体现圆的性质、相似性和几何构造。
以上提示语为根据原始绘图命令整理而来,仅供参考。