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Giải bài tập 5.43 trang 129 SGK Toán 9 tập 1 - Cùng khám phá

Từ điểm M vẽ tiếp tuyến MA đến đường tròn (O; 6cm) (A là tiếp điểm). Nếu \(MO = 10cm\) thì độ dài MA bằng A. 6cm. B. 7cm. C. 8cm. D. 9cm.

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

Toán - Văn - Anh
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Đề bài

Từ điểm M vẽ tiếp tuyến MA đến đường tròn (O; 6cm) (A là tiếp điểm). Nếu \(MO = 10cm\) thì độ dài MA bằng

A. 6cm. B. 7cm. C. 8cm. D. 9cm.

Phương pháp giải - Xem chi tiết

+ Chứng minh tam giác MAO vuông tại A. + Áp dụng định lí Pythagore vào tam giác MAO vuông tại A ta tính được MA.

Lời giải chi tiết

Vì MA là tiếp tuyến của (O) nên \(MA \bot AO\). Do đó, tam giác MAO vuông tại A. Suy ra: \(M{A^2} + A{O^2} = M{O^2}\) (định lí Pythagore), \(MA = \sqrt {M{O^2} - A{O^2}}  = \sqrt {{{10}^2} - {6^2}}  = 8\left( {cm} \right)\) Chọn C

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