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Giải bài 4 trang 89 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Cho góc vuông xOy có hai cạnh tiếp xúc với đường tròn (I; R) tại A, B. Cho biết chu vi của tứ giác OAIB bằng 20 cm. Tính R và độ dài AB.

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

Toán - Văn - Anh
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Đề bài

ඣCho góc vuông xOy có hai cạnh tiếp xúc với đường tròn (I; R) tại A, B. Cho biết chu vi của tứ giác OAIB bằng 20 cm. Tính R và độ dài AB.

Phương pháp giải - Xem chi tiết

Chứng minh OAIB là hình vuông rồi suy ra cạnh AB.

Lời giải chi tiết

Ta có Ox và Oy tiếp xúc với (I; R) lần lượt tại A và B, suy ra \(IA \bot Ox,IB \bot Oy,IA = IB = R.\) Tứ giác OAIB có ba góc vuông và có hai cạnh kề bằng nhau nên là hình vuông. Suy ra 4R = 20, suy ra R = 5 cm. Trong hình vuông OAIB ta có đường chéo AB = \(R\sqrt 2  = 5\sqrt 2 \) (cm).

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