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Giải Bài 5 trang 65 sách bài tập toán 7 - CTST

Cho hai đoạn thẳng AB và CD cắt nhau tại O. Tìm điểm M sao cho \(MA + MB + MC + M{\rm{D}}\) nhỏ nhất.

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Đề bài

Cho hai đoạn thẳng AB và CD cắt nhau tại O. Tìm điểm M sao cho \(MA + MB + MC + M{\rm{D}}\) nhỏ nhất.

Phương pháp giải - Xem chi tiết

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Lời giải chi tiết

Ta có: \(MA + MB \ge AB,MC + M{\rm{D}} \ge C{\rm{D}}\)Suy ra: \(MA + MB + MC + M{\rm{D}} \ge AB + C{\rm{D}}\)MA + MB + MC + MD nhỏ nhất khi và chỉ khi \(MA + MB + MC + M{\rm{D = }}AB + C{\rm{D}}\)Điều này xảy ra khi M trùng với điểm O.

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