928 Some geometry problems from recent journals
Mathematics Magazine, Problem 1669, proposed by A. N. Duman,
Bilkent University, Turkey
LetABCbe a triangle and letEbe the midpoint ofBC. A circle passing
throughAandCintersectsBAandBCin pointsGandErespectively.
LetDbe the midpoint ofEC. A line throughDand perpendicular to
BCintersectsACatF, with 3 AF =FC. Prove that triangleFDGis
similar to triangleABC.