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Giải bài tập 5.5 trang 90 SGK Toán 9 tập 1 - Kết nối tri thức

Cho nửa đường tròn đường kính AB và một điểm M tùy ý thuộc nửa đường tròn đó. Chứng minh rằng khoảng cách từ M đến AB không lớn hơn (frac{{AB}}{2}.)

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Cho nửa đường tròn đường kính AB và một điểm M tùy ý thuộc nửa đường tròn đó. Chứng minh rằng khoảng cách từ M đến AB không lớn hơn \(\frac{{AB}}{2}.\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Gọi H là hình chiếu của M trên AB. Khi đó khoảng cách từ M đến AB bằng độ dài đoạn MH. Xét tam giác MHO vuông tại H có: \(MH \le MO = \frac{{AB

Lời giải chi tiết

Gọi H là hình chiếu của M trên AB. Khi đó khoảng cách từ M đến AB bằng độ dài đoạn MH. Xét tam giác MHO vuông tại H có: \(MH \le MO\) Lại có: \(MO = \frac{{AB}}{2}\)(do AB là đường kính, OM là bán kính của đường tròn (O)). Vậy \(MH \le \frac{{AB}}{2}.\)

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