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Giải bài tập 4 trang 74 SGK Toán 9 tập 2 - Chân trời sáng tạo

Cho hình vuông MNPQ nội tiếp đường tròn bán kính R. Tính độ dài cạnh và đường chéo của hình vuông theo R.

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

Toán - Văn - Anh
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Đề bài

Cho hình vuông MNPQ nội tiếp đường tròn bán kính R. Tính độ dài cạnh và đường chéo của hình vuông theo R.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

-  Đọc kĩ dữ liệu để vẽ hình. -  Dựa vào: Đường tròn ngoại tiếp hình vuông có tâm là giao điểm của hai đường chéo và có bán kính bằng nửa đường chéo.

Lời giải chi tiết

Vì hình vuông MNPQ nội tiếp. O là giao điểm của MP và NQ  Suy ra R = OM = \(\frac{{MP}}{2}\). Do đó MP = 2R.

Ta có MN2 = OM2 + ON2 = R2 + R2 = 2R2

Suy ra MN = \(R\sqrt 2 \). Vậy hình vuông MNPQ có độ dài cạnh là \(R\sqrt 2 \), đường chéo là 2R.

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