From perspective of G, cross ratio R(A,F,E,B)=R(A,C,N,B) From perspective of D, cross ratio R(A,F,E,B)=R(A,M,C,B) Hence, (AB*NC)/(AN*BC) = (AB*MC)/(AC*MB) => NC / AN = MC / MB => MC=NC qed
To W Fung I note that your solution never use or require points A,B,D,E,F,G located on the same circle. Does that mean that problem gives extra information or I may miss something here ?. I appreciate if you can give all of us details explanation.
From my solution, "From perspective of G, cross ratio R(A,F,E,B)=R(A,C,N,B)"
The perspectivity holds when G lies on the circle of (AFEB). This should be the properties of the perspectivity. (the perspectivity is preserved under inversion)
For more information, please see: http://www.imomath.com/index.php?options=331
From perspective of G, cross ratio R(A,F,E,B)=R(A,C,N,B)
ReplyDeleteFrom perspective of D, cross ratio R(A,F,E,B)=R(A,M,C,B)
Hence, (AB*NC)/(AN*BC) = (AB*MC)/(AC*MB)
=> NC / AN = MC / MB
=> MC=NC
qed
To W Fung
DeleteI note that your solution never use or require points A,B,D,E,F,G located on the same circle. Does that mean that problem gives extra information or I may miss something here ?. I appreciate if you can give all of us details explanation.
Peter Tran
To peter tran,
ReplyDeleteFrom my solution, "From perspective of G, cross ratio R(A,F,E,B)=R(A,C,N,B)"
The perspectivity holds when G lies on the circle of (AFEB). This should be the properties of the perspectivity. (the perspectivity is preserved under inversion)
For more information, please see:
http://www.imomath.com/index.php?options=331
W Fung
Thank you for the explanation.
ReplyDeletePeter Tran