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Giải bài tập 5.7 trang 90 SGK Toán 9 tập 1 - Kết nối tri thức

Tâm O của một đường tròn cách dây AB của nó một khoảng 3 cm. Tính bán kính của đường tròn (O), biết rằng dây cung nhỏ AB có số đo bằng (100^circ )(làm tròn kết quả đến hàng phần mười).

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

Toán - Văn - Anh
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Đề bài

Tâm O của một đường tròn cách dây AB của nó một khoảng 3 cm. Tính bán kính của đường tròn (O), biết rằng dây cung nhỏ AB có số đo bằng \(100^\circ \)(làm tròn kết quả đến hàng phần mười).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Theo bài 5.6, \(\widehat {HOA} = \frac{{\widehat {AOB}}}{2} = \frac{{100^\circ }}{2} = 50^\circ \). Xét tam giác OAH vuông tại H từ đó tính được độ dài bán kính OA.

Lời giải chi tiết

Theo bài ra ta có sđ\(\overset\frown{AB}=100^\circ \). Kẻ OH là đường cao của tam giác OAB, H \(\in\) AB. Tam giác OAB cân tại O nên OH đồng thời là đường phân giác, khi đó: \(\widehat {HOA} = \widehat {HOB} = \frac{{\widehat {AOB}}}{2}\) mà \(\widehat {AOB} = \)sđ\(\overset\frown{AB}=100{}^\circ \) nên \(\widehat {HOA} = \frac{{100^\circ }}{2} = 50^\circ \) Xét tam giác OAH vuông tại H có: \(\cos \widehat {HOA} = \frac{{OH}}{{OA}} \Rightarrow OA = \frac{{OH}}{{\cos \widehat {HOA}}} = \frac{3}{{\cos 50^\circ }} \approx 4,7\)(cm)

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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