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Giải bài tập 9.12 trang 76 SGK Toán 9 tập 2 - Kết nối tri thức

Người ta muốn làm một khung gỗ tam giác đều để đặt vừa khít một chiếc đồng hồ hình tròn có đường kính 30cm (H.9.23). Hỏi độ dài các cạnh (phía bên trong) của khung gỗ phải bằng bao nhiêu?

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

Toán - Văn - Anh
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Đề bài

Người ta muốn làm một khung gỗ tam giác đều để đặt vừa khít một chiếc đồng hồ hình tròn có đường kính 30cm (H.9.23). Hỏi độ dài các cạnh (phía bên trong) của khung gỗ phải bằng bao nhiêu?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Gọi khung gỗ hình tam giác đều là tam giác ABC. Đồng hồ là đường tròn tâm I, có đường kính 30cm + Gọi H là giao điểm của AI và BC nên IH là bán kính đường tròn nội tiếp tam giác ABC. + Ta có: \(IH = \frac{{\sqrt 3 }}{6}BC\), từ đó tính được BC.

Lời giải chi tiết

Gọi khung gỗ hình tam giác đều là tam giác ABC. Đồng hồ là đường tròn tâm I, bán kính \(IH = \frac{{30}}{2} = 15cm\) Vì (I; IH) nội tiếp tam giác đều ABC nên \(IH = \frac{{\sqrt 3 }}{6}BC\), \(15 = \frac{{\sqrt 3 }}{6}BC\) nên \(BC = 30\sqrt 3 \left( {cm} \right)\) Vậy độ dài cạnh khung gỗ phía bên trong bằng \(30\sqrt 3 cm\).

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