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Angle Bisector Intersection and Cyclic Quadrilateral

Angle Bisector Intersection and Cyclic Quadrilateral
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2017-05-06 16:55
CircleAngleGeometric Construction
This example demonstrates the geometric construction of a cyclic quadrilateral using the intersection point of angle bisectors. Key math concepts include angle bisectors, intersection points, circles, cyclic quadrilaterals, and geometric constructions. The construction uses commands like Polygon, AngularBisector, Intersect, Circle, and Angle. It is suitable for high school mathematics education to understand the properties and construction methods of cyclic quadrilaterals.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. AngularBisector(A, D, C) → e
  3. AngularBisector(D, C, B) → f
  4. AngularBisector(C, B, A) → g
  5. AngularBisector(B, A, D) → h
  6. Intersect(h, g) → E
  7. Intersect(g, f) → F
  8. Intersect(e, f) → G
  9. Intersect(e, h) → H
  10. Polygon(H, G, F, E) → poly2, h_1, g_1, f_1, e_1
  11. Circle(H, G, F) → k
  12. Angle(poly2) → α, β, γ, δ