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Giải bài tập 7.22 trang 40 SGK Toán 9 tập 2 - Cùng khám phá

Hình vuông ABCD có cạnh 4 cm và hình chữ nhật MNPQ có chiều rộng 2 cm cùng nội tiếp trong đường tròn (O) (Hình 7.26). Tính chiều dài MQ của hình chữ nhật.

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

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Đề bài

Hình vuông ABCD có cạnh 4 cm và hình chữ nhật MNPQ có chiều rộng 2 cm cùng nội tiếp trong đường tròn (O) (Hình 7.26). Tính chiều dài MQ củ🐻a hình💯 chữ nhật.

 

Phương pháp giải - Xem chi tiết

Tính bán kính đường tròn ngoại tiếp hình vuông bằng nửa đường chéo. Suy ra bán kính ngoại tiếp hình chữ nhật, sau đó tính đường chéo hình chữ nhật để suy ra chiều dài hình♉ chữ nhật.

Lời giải chi tiết

Đường chéo hình vuông là: \(\sqrt {{4^2} + {4^2}}  = 4\sqrt 2 \)cm
Bán kính đường tròn ngoại tiếp hình vuông OA bằn𒈔⛦g nửa đường chéo là: \(2\sqrt 2 \)cm

Suy ra OM = OA = \(2\sqrt 2 \) cm, nên ta có: MP = 2. OM = \(4\sqrt 2 \) cm. Xét tam giác vuông MQP vuông tại Q, ta có: MQ = \(\sqrt {M{P^2} - Q{P^2}}  = \sqrt {{{\left( {4\sqrt 2 } \right)}^2} - {2^2}}  = 2\sqrt 7 \) cm.

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