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Giải bài 2 trang 95 SGK Toán 10 – Kết nối tri thức

Cho tam giác ABC. Có bao nhiêu điểm M thỏa mãn

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Đề bài

Cho tam giác ABC. Có bao nhiêu điểm M thỏa mãn \(\left| {\overrightarrow {MA}  + \overrightarrow {MB}  + \overrightarrow {MC} } \right| = 3\)? A. Vô số B. 1 C. 2 D. 3

Phương pháp giải - Xem chi tiết

Áp dụng tính chất trọng tâm G của tam giác ABC: \(\overrightarrow {MA}  + \overrightarrow {MB}  + \overrightarrow {MC}  = 3\overrightarrow {MG} \)

Lời giải chi tiết

Gọi G là trọng tâm của tam giác ABC, ta có: \(\overrightarrow {GA}  + \overrightarrow {GB}  + \overrightarrow {GC}  = \overrightarrow 0 \)\( \Rightarrow \overrightarrow {MA}  + \overrightarrow {MB}  + \overrightarrow {MC}  = 3\overrightarrow {MG}  + \overrightarrow {GA}  + \overrightarrow {GB}  + \overrightarrow {GC}  = 3\overrightarrow {MG} \)Do đó \(\left| {\overrightarrow {MA}  + \overrightarrow {MB}  + \overrightarrow {MC} } \right| = 3 \Leftrightarrow \left| {3\overrightarrow {MG} } \right| = 3\) hay \(MG = 1\)Vậy tập hợp các điểm M thỏa mãn là đường tròn tâm G, bán kính 1.Nói cách khác có vô số điểm M thỏa mãn ycbt.Chọn A.

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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