Viet Nam hexagon Theorem

Let hexagon ABCDEF. AC meets BD at G, BE meets CF at H, AE meets DF at I. GB/GD*ID/IF*HF/HC*GC/GA*IA/IF*HF/HB=1 <=> G,H,I are collinear (1) GB/GD*ID/IF*HF/HC*GC/GA*IA/IF*HF/HB=1 <=> A,B,C,D,E,F lie on a conic (2) G,H,I are collinear <=> A,B,C,D,E,F lie on a conic (3) (Pascal theorem) I named (1) and (2) are Viet Nam hexagon theorem. (This is a generalization power of a point with conic)

 

Đào Thanh Oai

 
Material Type
Activity
Tags
hexagon  theorem  conic  collinear 
Target Group (Age)
19+
Language
English (United States)
 
 
GeoGebra version
4.2
Views
1608
Report a problem
 
 
© 2018 International GeoGebra Institute