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Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1167.
Since D is on circumcicle of ABC => GHN is Simson line from D So G,H,N are collinearSince D is on circumcicle of AEF => GHM is Simson line from D So G,H,M are collinear => G,H,M,N are collinear
< DCH = < DAG = < GHD and since DHMC is con cyclic G,H,N are collinear Further < GDM = < ADF and because GDME and ADFE are cyclic < ADG = < FDM and so < AHG = < MHF so G,H, M are collinear Hence G,H, N, M are collinearSumith PeirisMoratuwa Sri Lanka
Sumith,There's seems to be a typo in your proof. Should it not be < DCB (not DCH) = < DAG = < GHD? As also D,H,N,C are concyclic not DHMC? Correct me if I'm wrong.By the way, I need your assistance in planning a trip to Sri Lanka coming summer in April/May 2016. Would you be kind enough to send me a message at: email@example.com?Ajit
Sorry Ajith I saw your post only nowBoth typos u pointed out are correct. Thank uWelcome to Sri Lanka. I have already sent u a Test mail. Do contact me if u do not receive same