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Giải bài tập 5.20 trang 103 SGK Toán 9 tập 1 - Kết nối tri thức

Bạn Thanh cắt 4 hình tròn bằng giấy có bán kính lần lượt là 4 cm, 6 cm, 7 cm và 8 cm để dán trang trí trên một mảnh giấy, trên đó có vẽ trước hai đường thẳng a và b.

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

Toán - Văn - Anh
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Đề bài

Bạn Thanh cắt 4 hình tròn bằng giấy có bán kính lần lượt là 4 cm, 6 cm, 7 cm và 8 cm để dán trang trí trên một mảnh giấy, trên đó có vẽ trước hai đường thẳng a và b. Biết rằng a và b là hai đường thẳng song song với nhau và cách nhau một khoảng 6 cm (nghĩa là mọi điểm trên đường thẳng b đều cách a một khoảng 6 cm). Hỏi nếu bạn Thanh dán sao cho tâm của cả 4 hình tròn đều nằm trên đường thẳng b thì hình tròn nào sẽ che khuất một phần của đường thẳng a, hình tròn nào sẽ không che khuất một phần của đường thẳng a?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Cho đường thẳng a và đường tròn (O; R). Gọi d là khoảng cách từ O đến a. Khi đó: + Đường thẳng a và đường tròn (O; R) cắt nhau khi \(d < R\). + Đường thẳng a và đường tròn (O; R) tiếp xúc với nhau khi \(d = R\). + Đường thẳng a và đường tròn (O; R) không giao nhau khi \(d > R\).

Lời giải chi tiết

Giả sử bốn hình tròn bằng giấy có tâm lần lượt là A, B, C và D. Khi đó, ta có các đường tròn (A; 4cm), (B; 6cm), (C; 7cm), (D; 8cm). Tâm của các đường tròn này thuộc đường thẳng b nên đều cách a một khoảng \(d = 6cm\). + Đường tròn (A; 4cm) có bán kính 4cm < d nên đường tròn (A; 4cm) không giao đường thẳng a. + Đường tròn (B; 6cm) có bán kính 6cm=d nên đường tròn (B; 6cm) tiếp xúc với đường thẳng a. + Đường tròn (C; 7cm) có bán kính 7cm>d nên đường tròn (C; 7cm) cắt đường thẳng a. + Đường tròn (D; 8cm) có bán kính 8cm>d nên đường tròn (D; 8cm) cắt đường thẳng a. Từ đó các hình tròn bán kính 4cm, 6cm không đè lên đường thẳng a; các hình tròn bán kính 7cm, 8cm đè lên đường thẳng a.

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

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