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Giải bài tập 5.13 trang 110 SGK Toán 9 tập 1 - Cùng khám phá

Cho đường tròn (O; 12cm) và điểm A cách O là 8cm. Hãy xác định vị trí tương đối của (O) và đường thẳng d đi qua A vuông góc OA.

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

Toán - Văn - Anh
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Đề bài

Cho đường tròn (O; 12cm) và điểm A cách O là 8cm. Hãy xác định vị trí tương đối của (O) và đường thẳng d đi qua A vuông góc OA.

Phương pháp giải - Xem chi tiết

Cho đường tròn (O; R) và đường thẳng a. Đặt d là khoảng cách từ O đến đường thẳng a. Vị trí tương đối của đường thẳng a và đường tròn (O; R) có thể được xác định dựa vào mối quan hệ giữa R và d như sau: + Nếu \(d > R\) thì đường thẳng a và đường tròn (O) không giao nhau. + Nếu \(d = R\) thì đường thẳng a và đường tròn (O) tiếp xúc nhau. + Nếu \(d < R\) thì đường thẳng a và đường tròn (O) cắt nhau.

Lời giải chi tiết

Vì d là đường thẳng đi qua A và vuông góc với OA nên khoảng cách từ O đến đường thẳng d là \(OA = 8cm\). Vì \(8cm < 12cm\) nên đường thẳng d và đường tròn (O) cắt nhau.

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