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Quadrilaterals and Circumcenter

Quadrilaterals and Circumcenter
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2017-07-18 06:51
CirclePolygonGeometric Construction
This example demonstrates the relationship between quadrilaterals and circumcenters. Key mathematical concepts include quadrilaterals, circumcenters, orthocenters, and circumcircles. Using GeoGebra commands such as Point, Element, If, Vector, etc., the construction of a quadrilateral and its circumcircle is shown, along with the properties of the orthocenter. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Element(hlist_1, n) → h
  3. If(n ≟ 1, (2, f1(y(A))), (2, f2(y(A)))) → B
  4. Vector(A, B) → u
  5. Vector(B, C) → v
  6. Textfield(f1) → inputBox1
  7. Textfield(f2) → inputBoxf
  8. Vector(A, C) → w
  9. Sequence(k, k, -4, 4, dx) → x_*
  10. Zip((y(A) + k, h(y(A) + k)), k, x_*) → hptlist
  11. Element(f1list, n) → f
  12. Zip(Vector[(0, k), (x(C), h(k))], k, x_*) → hlist
  13. Zip(Vector[(0, k), (x(B), f(k))], k, x_*) → glist
  14. Zip(Vector[(x(B), f(k)), (x(C), h(k))], k, x_*) → fglist