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Geometry Problem 804, Step by step IllustrationClick the figure to see the interactive illustration
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=NCqed
To W FungI 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, 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=331W Fung
Thank you for the explanation.Peter Tran