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Cho tam giác ABC, trên AB lấy điểm M sao cho AM = ¼ AB

Cho tam giác ABC. Trên AB lấy điểm M sao cho AM = ¼ AB. Nối CM. Trên CM lấy điểm G sao cho GM = 1/3 CM. Nối AG cắt BC tại N. Biết diện tích tam giác ABC bằng 120 cm vuông. Tính tỉ số BN/CN
 
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Tham khảo câu trả lời từ Trợ lý ảo Lazi
Gọi H là giao điểm của AG và CM.
Ta có: AM = 1/4 AB, GM = 1/3 CM
=> AH = 3/4 AM = 3/4 * 1/4 AB = 3/16 AB
=> GH = GM + HM = 1/3 CM + 3/16 AB = 1/3 * 4/3 AB + 3/16 AB = 17/16 AB
Áp dụng định lí Ceva ta có:
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1
1
Tiến Dũng
18/04 21:16:34
+5đ tặng

a: S ABM=1/4*S ABC=30cm2

b: Kẻ MK//AN

Xét ΔANC có MK//AN

nên CK/CN=CM/CA=3/4

=>CK=3/4CN

=>NK=1/4CN

Xét ΔBMK có GN//MK

nên BN/BK=BG/BM=2/3

=>BN=2/3BK

=>BK=3/2BN

=>NK=1/3BK

=>1/4CN=1/3BK

=>CN/BK=1/3:1/4=4/3

=>CN=4/3BK=4/3*3/2BN=4/2BN=2BN

=>BN/CN=1/2

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