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Quadrilateral Centroid and Circumcircle Demo

Quadrilateral Centroid and Circumcircle Demo
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2020-01-23 11:08
CirclePolygonGeometric Construction
This example demonstrates how to draw the centroid and circumcircle of a general quadrilateral. Key math concepts include quadrilaterals, centroid, circumcircle, and geometric construction. It uses commands like Point, Polygon, Circle, Centroid, Line, Intersect in GeoGebra. Suitable for high school students learning geometric constructions and quadrilateral properties.

GeoGebra Commands & Parameters

  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