Viet Nam hexagon Theorem
- Author:
- Đào Thanh Oai
Let hexagon ABCDEF. AC meets BD at G, BE meets CF at H, AE meets DF at I then
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)