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Vì \(M\)trung điểm của \(AB\Rightarrow AM=BM\)
\(OA+OB=OB+OB+AB=2OB+BM+BM=2OB+2BM\)(1)
\(OM=OB+BM\) (2)
Từ (1) và (2) \(\Rightarrow\frac{OA+AB}{OM}=\frac{2OB+2BM}{OB+BM}=\frac{2\left(OB+BM\right)}{OB+BM}=2\)
Mặt khác \(OM=\frac{OA+OB}{2}\)
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Ta có:
2OM=OM+OM=(OA+AM)+(OB−BM)=OA+OB+(AM−BM)2OM=OM+OM=(OA+AM)+(OB−BM)=OA+OB+(AM−BM)
Vì M là trung điểm AB
=> AM=BM
=> 2OM=OA+OB2OM=OA+OB
=> OM=OA+OB2
\(OM< \frac{OA+OB}{2}\) KO BIẾT LÝ LUẬN NHƯNG BIẾT SO SÁNH
lập luân.....để:
OM= OA + BM ( VÌ AM=BM )
+
OM= OB - BM
=> 2.OM= OA + BM + OB - BM
=> OM = ( OA + OB ) : 2