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Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 677.
http://img542.imageshack.us/img542/4607/problem677.pngExtend FE to cut BC at H ( see picture)Let AD=BC=a and DF=2aTriangle EMC similar to tri. EDA ( case AA) So EM/MD=MC/AD=1/2Triangle EMH similar to tri. EDF ( case AA) So MH/DF=ME/ED=1/2 and MH=a , CH=1.5aTriangle GCH similar to tri. GDF so CH/DF=GC/GD=1.5a/2a = 3/x x=4Peter Tran
Draw DH parallel FE (E on AC). Thenx/3 = HE/EC = (HE/AE)(AE/EC) = (DF/AF)(AD/MC)= (2/3)(2)= 4/3x = 4