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Giải bài 3 trang 85 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Xác định vị trí tương đối của hai đường tròn (O; R) và (O’; R’) trong mỗi trường hợp sau: a) OO’ = 7, R = 29, R’ = 4; b) OO’ = 21, R = 44, R’ = 23; c) OO’ = 15, R = 7, R’ = 8; d) OO’ = 6, R = 24, R’ = 20;

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

Toán - Văn - Anh
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Đề bài

Xác định vị trí tương đối của hai đường tròn (O; R) và (O’ꦰ; R’) trong mỗi trường hợp sau:

a) OO’ = 7, R = 29, R’ = 4;

b) OO’ = 21, R = 44, R’ = 23;

c) OO’ = 15, R = 7, R’ = 8;

d) OO’ = 6, R = 24, R’ = 20;

Phương pháp giải - Xem chi tiết

Dựa vào: Hai đường tròn cắt nhau: R – R’ < OO’ < R + R’ Hai đường tròn tiếp xúc ngoài: OO’ = R + R’ Hai đường tròn tiếp xúc trong: OO’ = R - R’ Hai đường tròn ở ngoài nhau: OO’ > R + R’ Đường tròn (O; R) đựng đường tròn (O’; R’): OO’ < R – R’.

Lời giải chi tiết

a) Ta có 7 < 29 – 4 nên OO’ < R – R’, suy ra đường tròn (O; R) đựng đường tròn (O’; R’). b) Ta có 21 = 44 – 23 nên OO’ = R – R’, suy ra hai đường tròn (O; R) và (O’; R’) tiếp xúc trong. c) Ta có 15 = 7 + 8 nên OO’ = R + R’, suy ra hai đường tròn (O; R) và (O’; R’) tiếp xúc ngoài. d) Ta có 24 – 20 < 6 < 24 + 20 nên R – R’ < OO’ < R + R’, suy ra hai đường tròn (O; R) và (O’; R’) cắt nhau.

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