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四边形重心与外接圆演示

四边形重心与外接圆演示
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2020-01-23 11:08
圆多边形几何作图
①本范例演示了如何在一个四边形中绘制其重心和外接圆；②涉及的核心数学概念包括四边形、重心、外接圆、几何作图；③作图要点——使用了Point, Polygon, Circle, Centroid, Line, Intersect等GeoGebra命令和对象来构建图形；④适合高中阶段学习几何作图和四边形性质的学生。

GeoGebra 命令及参数

  1. Point(Circle[M, a]) → N
  2. Polygon(M, N, 4) → poly3, r, s, t, c, O, P
  3. Cube(poly3, true) → d, K, edgeKM, edgePR, edgeKR, edgeKL, edgeLN, edgeLQ, edgeOQ, edgeQR, L, Q, R, faceKMPR, faceKLNM, faceLNOQ, faceOPRQ, faceKLQR
  4. Midpoint(R, P) → W
  5. Midpoint(Q, R) → V
  6. Midpoint(Q, O) → U
  7. Circle(U, V, W) → e
  8. Point(e) → C_1
  9. Polygon(Q, R, P, O) → q2, q_1, r_1, p, o
  10. Centroid(q2) → T
  11. Line(C_1, T) → l
  12. Intersect(l, e, 1) → E_1
  13. PointIn(Sphere[A, a]) → B
  14. Polygon(A, B, 4, xOyPlane) → poly1, g, h, i, j, C, D
  15. Cube(poly1, true) → b, G, edgeAG, edgeDJ, edgeGJ, edgeGH, edgeBH, edgeHI, edgeCI, edgeIJ, H, I, J, faceADJG, faceABHG, faceBCIH, faceCDJI, faceGHIJ
  16. Midpoint(J, D) → B_1
  17. Midpoint(I, J) → A_1
  18. Midpoint(I, C) → Z
  19. Circle(Z, A_1, B_1) → k
  20. Point(k) → D_1
  21. Segment(E_1, D_1) → k_1
  22. Segment(C_1, D_1) → g_1
  23. Polygon(I, J, D, C) → q1, ı, j_1, d_1, c_1
  24. Centroid(q1) → S
  25. Segment(E_1, S) → l_1
  26. Segment(C_1, S) → h_1
  27. Line(D_1, S) → m
  28. Intersect(m, k, 1) → F_1
  29. Segment(E_1, F_1) → m_1
  30. Segment(C_1, F_1) → i_1
  31. Segment(A, B) → f
  32. Point(Circle[E, a, xOyPlane]) → F
  33. Segment(M, N) → q
  34. Segment(C_1, E_1) → n
  35. Segment(D_1, F_1) → f_1