KHÔNG CẦN GIẢI RA, CHỈ CẦN NHẬN XÉT LỜI GIẢI ĐÚNG HAY SAI MỘT CÁCH TỈ MỈ LÀ ĐƯỢC!!! TỈ MỈ, RÕ RÀNG NHA, CẢM ƠN!!! đề bài: cho tam giác ABC. điểm D chia trong AB theo tỉ số 1:2, Echia trong AC theo tỉ số 2:5 DEgiao BC tại F. Tính BF:FC? GIẢI: Qua B kẻ BK //EC giao EF=K(K thuộc EF); qua B kẻ BM//EF giao AC=M(M thuộc AC). vì tam giác ECF có BM//EF=> FB/FC=EM/EC (theo định lý Ta lét) vì tam giác EFC có BK//EF( giả thiết) =>> FK/EF=FB/FC=KB/EC(hệ quả định lý Ta lét) Vì điểm D chia trong AB theo tỉ số 1:2=>AD/DB=1/2=>AD/AB=AD/(DB+AD)=1/(1+2)=1/3 vì điểm E chia trong AC theo tỉ số 2:5=>AE/EC=2/5=>AE/AC=AE/(EC+AE)=2/(5+2)=2/7 vì tam giác ABM có DE//BM(BM//EF mà D lại thuộc EF) => AD/BD=AE/EM=>>AE/EM=1/2=>FM=2AE (1) vì AE/EC=2/5(giả thiết)=>EC=5AE/2 (2) từ (1) và(2)=> EM/EC=2AE/5AE/2=4/5 vì FB/FC=EM/EC(chứng minh trên)=> FB/FC=4/5

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