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Giải bài tập 5.25 trang 107 SGK Toán 9 tập 1 - Kết nối tri thức

Cho hai điểm O và O’ cách nhau một khoảng 5 cm. Mỗi đường tròn sau đây có vị trí tương đối như thế nào đối với đường tròn (O; 3 cm) . a) Đường tròn (O’; 3 cm) ; b) Đường tròn (O’; 1 cm) c) Đường tròn (O’; 8 cm)

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

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Đề bài

Cho hai điểm O và O’ cách nhau một khoảng 5 cm. Mỗi đường tròn sau đây có vị trí tương đối như thế nào đối với đường tròn (O; 3 cm) . a) Đường tròn (O’; 3 cm) b) Đường tròn (O’; 1 cm) c) Đường tròn (O’; 8 cm) 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Nếu R – R’ < OO’ < R + R’ thì hai đường tròn (O; R) và (O’; R’) cắt nhau. + Nếu OO’ = R + R’ thì hai đường tròn (O; R) và (O’; R’) tiếp xúc ngoài. + Nếu OO’ = R – R’ > 0 thì hai đường tròn (O; R) và (O’; R’) tiếp xúc trong. + Nếu OO’ > R + R’ thì hai đường tròn (O; R) và (O’; R’) ngoài nhau. + Nếu OO’ < R – R’ thì hai đường tròn (O; R) đựng đường tròn (O’; R’) .

Lời giải chi tiết

Ta có: OO’ = 5 cm a) Vì 3 – 3 < 5 < 3 + 3 hay 0 < 1 < 6 nên hai đường tròn (O; 3 cm) và (O’; 3 cm) cắt nhau. b) Vì 5 > 3 + 1 > 3 – 1 hay 5 > 4 > 2 nên hai đường tròn (O; 3 cm) và (O’; 1 cm) nằm ngoài nhau. c) Vì 8 + 3 > 5 = 8 – 3 hay 11 > 5 = 5 nên hai đường tròn (O; 3 cm) và (O’; 8 cm) tiếp xúc trong.

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