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Giải bài 4 trang 79 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Cho tam giác đều MNP có cạnh bằng (2asqrt 3 ). Tính theo a bán kính các đường tròn ngoại tiếp và nội tiếp tam giác MNP.

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

Toán - Văn - Anh
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Đề bài

Cho tam giác đều MNP có cạnh bằng \(2a\sqrt 3 \). Tính theo a bán kính các đường trò🌼n ngoại tiếp và nội tiếp tam giác MNP.

Phương pháp giải - Xem chi tiết

Đường tròn ngoại tiếp tam giác đều cạnh a có tâm là trọng tâm của tam giác và bán kính bằng \(\frac{{a\sqrt 3 }}{3}\). Đường tròn nội tiếp tam giác đều cạnh a có tâm là trọng tâm của tam giác và bán kính bằng \(\frac{{a\sqrt 3 }}{6}\).

Lời giải chi tiết

Gọi G là trọng tâm, MH là đường cao của tam giác đều MNP. Khi đó, đường tròn (G; MG) là đường tròn ngoại tiếp tam giác đều MNP; đường tròn (G; GH) là đường tròn nội tiếp tam giác đều MNP. Do đó: \(MG = \frac{{2a\sqrt 3.\sqrt 3 }}{3} = 2a\). \(GH = \frac{{2a\sqrt 3.\sqrt 3 }}{6} = a\).

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