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Giải bài tập 1 trang 68 SGK Toán 9 tập 2 - Chân trời sáng tạo

Cho tam giác đều ABC có cạnh bằng 6 cm. a) Nêu các vẽ đường tròn ngoại tiếp tam giác ABC. b) Nêu các vẽ đường tròn nội tiếp tam giác ABC. c) Tính bán kính R của đường tròn ngoại tiếp và bán kính r của đường tròn nội tiếp tam giác ABC.

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

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Đề bài

Cho tam giác đều ABC có cạnh bằng 6 cm.

a) Nêu các vẽ đường tròn ngoại tiếp tam giác ABC.

b) Nêu các vẽ đường tròn nội tiếp tam giác ABC.

c) Tính bán kính R của đường tròn ngoại tiếp và bá🥂n kính r của đường tròn nội tiếp tam giác ABC.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

-  Đọc kĩ dữ kiện đề bài để vẽ hình. -  Dựa vào đường tròn ngoại tiếp có tâm là giao điểm của ba đường trung trực của tam giác và có bán kính bằng khoảng cách từ giao điểm đó đến một đỉnh bất kì của tam giác. -  Dựa vào: Đường tròn nội tiếp tam giác có tâm là giao điểm của ba đường phân giác trong và bán kính bằng khoảng cách từ giao điểm đó đến một cạnh bất kì của tam giác.

Lời giải chi tiết

a) Kẻ ba đường trung trực AH, BK, CE của tam giác ABC, ba đường đó đồng quy tại điểm O suy ra O là tâm đường tròn ngoại tiếp tam giác ABC, bán kính OA = R.

b) Vì tam giác ABC đều nên các đường trung trực của tam giác cũng đồng thời là đường phân giác suy ra O cũng là tâm đường tròn nội tiếp tam giác ABC, bán kính OH = r. c) Bán kính đường tròn ngoại tiếp tam giác ABC là: R = OA = \(\frac{{a\sqrt 3 }}{3} = \frac{{6\sqrt 3 }}{3} = 2\sqrt 3 \) (cm). Bán kính đường tròn nội tiếp tam giác ABC là: r = OH = \(\frac{{a\sqrt 3 }}{6} = \frac{{6\sqrt 3 }}{6} = \sqrt 3 \) (cm).

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