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Nội dung: <blockquote data-quote="blackbaby" data-source="post: 122227" data-attributes="member: 58755">Hình học 10: Chứng minh ba điểm thẳng hàng.1. Cho<img src="https://codecogs.izyba.com/png.latex?\150dpi \Delta ABC" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> . I,J là hai điểm thỏa mãn:<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{IA}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi =" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> <img src="https://codecogs.izyba.com/png.latex?\150dpi 2" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{IB}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />, <img src="https://codecogs.izyba.com/png.latex?\150dpi 3" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{JA}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi +" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi 2" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{JC}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi =" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> <img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{0}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> . Tính <img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{IJ}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> theo <img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{AB}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />,<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{AC}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />.2. Cho tứ giác <img src="https://codecogs.izyba.com/png.latex?\150dpi ABCD" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />, G là trọng tâm. A',B',C',D' lần lượt là trọng tâm của tam giác BCD,ACD,ABD,ABC.a/ Chứng minh G  là điểm chung của AA',BB',CC',DD'.b/ G chia AA',BB',CC',DD' theo tỷ số nào?3/ Cho tam giác ABC. Lấy M,N,P thỏa mãn:<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{MB}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi =" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi 3" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{MC}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />,<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{NA}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi +" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi 3" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{NC}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi =\vec{0}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />,<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{PA}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi +\vec{PB}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\150dpi =\vec{0}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Tìm<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{MP}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />,<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{MN}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> theo <img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{AB}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />,<img src="https://codecogs.izyba.com/png.latex?\150dpi \vec{AC}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> .Suy ra M,N,P thẳng hàng.</blockquote>

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